+#undef PW
+#define PW isl_pw_qpolynomial
+#undef EL
+#define EL isl_qpolynomial
+#undef IS_ZERO
+#define IS_ZERO is_zero
+#undef FIELD
+#define FIELD qp
+
+#include <isl_pw_templ.c>
+
+#undef UNION
+#define UNION isl_union_pw_qpolynomial
+#undef PART
+#define PART isl_pw_qpolynomial
+#undef PARTS
+#define PARTS pw_qpolynomial
+
+#include <isl_union_templ.c>
+
+int isl_pw_qpolynomial_is_one(__isl_keep isl_pw_qpolynomial *pwqp)
+{
+ if (!pwqp)
+ return -1;
+
+ if (pwqp->n != -1)
+ return 0;
+
+ if (!isl_set_fast_is_universe(pwqp->p[0].set))
+ return 0;
+
+ return isl_qpolynomial_is_one(pwqp->p[0].qp);
+}
+
+__isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
+ __isl_take isl_pw_qpolynomial *pwqp1,
+ __isl_take isl_pw_qpolynomial *pwqp2)
+{
+ int i, j, n;
+ struct isl_pw_qpolynomial *res;
+ isl_set *set;
+
+ if (!pwqp1 || !pwqp2)
+ goto error;
+
+ isl_assert(pwqp1->dim->ctx, isl_dim_equal(pwqp1->dim, pwqp2->dim),
+ goto error);
+
+ if (isl_pw_qpolynomial_is_zero(pwqp1)) {
+ isl_pw_qpolynomial_free(pwqp2);
+ return pwqp1;
+ }
+
+ if (isl_pw_qpolynomial_is_zero(pwqp2)) {
+ isl_pw_qpolynomial_free(pwqp1);
+ return pwqp2;
+ }
+
+ if (isl_pw_qpolynomial_is_one(pwqp1)) {
+ isl_pw_qpolynomial_free(pwqp1);
+ return pwqp2;
+ }
+
+ if (isl_pw_qpolynomial_is_one(pwqp2)) {
+ isl_pw_qpolynomial_free(pwqp2);
+ return pwqp1;
+ }
+
+ n = pwqp1->n * pwqp2->n;
+ res = isl_pw_qpolynomial_alloc_(isl_dim_copy(pwqp1->dim), n);
+
+ for (i = 0; i < pwqp1->n; ++i) {
+ for (j = 0; j < pwqp2->n; ++j) {
+ struct isl_set *common;
+ struct isl_qpolynomial *prod;
+ common = isl_set_intersect(isl_set_copy(pwqp1->p[i].set),
+ isl_set_copy(pwqp2->p[j].set));
+ if (isl_set_fast_is_empty(common)) {
+ isl_set_free(common);
+ continue;
+ }
+
+ prod = isl_qpolynomial_mul(
+ isl_qpolynomial_copy(pwqp1->p[i].qp),
+ isl_qpolynomial_copy(pwqp2->p[j].qp));
+
+ res = isl_pw_qpolynomial_add_piece(res, common, prod);
+ }
+ }
+
+ isl_pw_qpolynomial_free(pwqp1);
+ isl_pw_qpolynomial_free(pwqp2);
+
+ return res;
+error:
+ isl_pw_qpolynomial_free(pwqp1);
+ isl_pw_qpolynomial_free(pwqp2);
+ return NULL;
+}
+
+__isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
+ __isl_take isl_pw_qpolynomial *pwqp)
+{
+ int i;
+
+ if (!pwqp)
+ return NULL;
+
+ if (isl_pw_qpolynomial_is_zero(pwqp))
+ return pwqp;
+
+ pwqp = isl_pw_qpolynomial_cow(pwqp);
+ if (!pwqp)
+ return NULL;
+
+ for (i = 0; i < pwqp->n; ++i) {
+ pwqp->p[i].qp = isl_qpolynomial_neg(pwqp->p[i].qp);
+ if (!pwqp->p[i].qp)
+ goto error;
+ }
+
+ return pwqp;
+error:
+ isl_pw_qpolynomial_free(pwqp);
+ return NULL;
+}
+
+__isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
+ __isl_take isl_pw_qpolynomial *pwqp1,
+ __isl_take isl_pw_qpolynomial *pwqp2)
+{
+ return isl_pw_qpolynomial_add(pwqp1, isl_pw_qpolynomial_neg(pwqp2));
+}
+
+__isl_give struct isl_upoly *isl_upoly_eval(
+ __isl_take struct isl_upoly *up, __isl_take isl_vec *vec)
+{
+ int i;
+ struct isl_upoly_rec *rec;
+ struct isl_upoly *res;
+ struct isl_upoly *base;
+
+ if (isl_upoly_is_cst(up)) {
+ isl_vec_free(vec);
+ return up;
+ }
+
+ rec = isl_upoly_as_rec(up);
+ if (!rec)
+ goto error;
+
+ isl_assert(up->ctx, rec->n >= 1, goto error);
+
+ base = isl_upoly_rat_cst(up->ctx, vec->el[1 + up->var], vec->el[0]);
+
+ res = isl_upoly_eval(isl_upoly_copy(rec->p[rec->n - 1]),
+ isl_vec_copy(vec));
+
+ for (i = rec->n - 2; i >= 0; --i) {
+ res = isl_upoly_mul(res, isl_upoly_copy(base));
+ res = isl_upoly_sum(res,
+ isl_upoly_eval(isl_upoly_copy(rec->p[i]),
+ isl_vec_copy(vec)));
+ }
+
+ isl_upoly_free(base);
+ isl_upoly_free(up);
+ isl_vec_free(vec);
+ return res;
+error:
+ isl_upoly_free(up);
+ isl_vec_free(vec);
+ return NULL;
+}
+
+__isl_give isl_qpolynomial *isl_qpolynomial_eval(
+ __isl_take isl_qpolynomial *qp, __isl_take isl_point *pnt)
+{
+ isl_vec *ext;
+ struct isl_upoly *up;
+ isl_dim *dim;
+
+ if (!qp || !pnt)
+ goto error;
+ isl_assert(pnt->dim->ctx, isl_dim_equal(pnt->dim, qp->dim), goto error);
+
+ if (qp->div->n_row == 0)
+ ext = isl_vec_copy(pnt->vec);
+ else {
+ int i;
+ unsigned dim = isl_dim_total(qp->dim);
+ ext = isl_vec_alloc(qp->dim->ctx, 1 + dim + qp->div->n_row);
+ if (!ext)
+ goto error;
+
+ isl_seq_cpy(ext->el, pnt->vec->el, pnt->vec->size);
+ for (i = 0; i < qp->div->n_row; ++i) {
+ isl_seq_inner_product(qp->div->row[i] + 1, ext->el,
+ 1 + dim + i, &ext->el[1+dim+i]);
+ isl_int_fdiv_q(ext->el[1+dim+i], ext->el[1+dim+i],
+ qp->div->row[i][0]);
+ }
+ }
+
+ up = isl_upoly_eval(isl_upoly_copy(qp->upoly), ext);
+ if (!up)
+ goto error;
+
+ dim = isl_dim_copy(qp->dim);
+ isl_qpolynomial_free(qp);
+ isl_point_free(pnt);
+
+ return isl_qpolynomial_alloc(dim, 0, up);
+error:
+ isl_qpolynomial_free(qp);
+ isl_point_free(pnt);
+ return NULL;
+}
+
+int isl_upoly_cmp(__isl_keep struct isl_upoly_cst *cst1,
+ __isl_keep struct isl_upoly_cst *cst2)
+{
+ int cmp;
+ isl_int t;
+ isl_int_init(t);
+ isl_int_mul(t, cst1->n, cst2->d);
+ isl_int_submul(t, cst2->n, cst1->d);
+ cmp = isl_int_sgn(t);
+ isl_int_clear(t);
+ return cmp;
+}
+
+int isl_qpolynomial_le_cst(__isl_keep isl_qpolynomial *qp1,
+ __isl_keep isl_qpolynomial *qp2)
+{
+ struct isl_upoly_cst *cst1, *cst2;
+
+ if (!qp1 || !qp2)
+ return -1;
+ isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), return -1);
+ isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), return -1);
+ if (isl_qpolynomial_is_nan(qp1))
+ return -1;
+ if (isl_qpolynomial_is_nan(qp2))
+ return -1;
+ cst1 = isl_upoly_as_cst(qp1->upoly);
+ cst2 = isl_upoly_as_cst(qp2->upoly);
+
+ return isl_upoly_cmp(cst1, cst2) <= 0;
+}
+
+__isl_give isl_qpolynomial *isl_qpolynomial_min_cst(
+ __isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2)
+{
+ struct isl_upoly_cst *cst1, *cst2;
+ int cmp;
+
+ if (!qp1 || !qp2)
+ goto error;
+ isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), goto error);
+ isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), goto error);
+ cst1 = isl_upoly_as_cst(qp1->upoly);
+ cst2 = isl_upoly_as_cst(qp2->upoly);
+ cmp = isl_upoly_cmp(cst1, cst2);
+
+ if (cmp <= 0) {
+ isl_qpolynomial_free(qp2);
+ } else {
+ isl_qpolynomial_free(qp1);
+ qp1 = qp2;
+ }
+ return qp1;
+error:
+ isl_qpolynomial_free(qp1);
+ isl_qpolynomial_free(qp2);
+ return NULL;
+}
+
+__isl_give isl_qpolynomial *isl_qpolynomial_max_cst(
+ __isl_take isl_qpolynomial *qp1, __isl_take isl_qpolynomial *qp2)
+{
+ struct isl_upoly_cst *cst1, *cst2;
+ int cmp;
+
+ if (!qp1 || !qp2)
+ goto error;
+ isl_assert(qp1->dim->ctx, isl_upoly_is_cst(qp1->upoly), goto error);
+ isl_assert(qp2->dim->ctx, isl_upoly_is_cst(qp2->upoly), goto error);
+ cst1 = isl_upoly_as_cst(qp1->upoly);
+ cst2 = isl_upoly_as_cst(qp2->upoly);
+ cmp = isl_upoly_cmp(cst1, cst2);
+
+ if (cmp >= 0) {
+ isl_qpolynomial_free(qp2);
+ } else {
+ isl_qpolynomial_free(qp1);
+ qp1 = qp2;
+ }
+ return qp1;
+error:
+ isl_qpolynomial_free(qp1);
+ isl_qpolynomial_free(qp2);
+ return NULL;
+}
+
+__isl_give isl_qpolynomial *isl_qpolynomial_insert_dims(
+ __isl_take isl_qpolynomial *qp, enum isl_dim_type type,
+ unsigned first, unsigned n)
+{
+ unsigned total;
+ unsigned g_pos;
+ int *exp;
+
+ if (n == 0)
+ return qp;
+
+ qp = isl_qpolynomial_cow(qp);
+ if (!qp)
+ return NULL;
+
+ isl_assert(qp->div->ctx, first <= isl_dim_size(qp->dim, type),
+ goto error);
+
+ g_pos = pos(qp->dim, type) + first;
+
+ qp->div = isl_mat_insert_cols(qp->div, 2 + g_pos, n);
+ if (!qp->div)
+ goto error;
+
+ total = qp->div->n_col - 2;
+ if (total > g_pos) {
+ int i;
+ exp = isl_alloc_array(qp->div->ctx, int, total - g_pos);
+ if (!exp)
+ goto error;
+ for (i = 0; i < total - g_pos; ++i)
+ exp[i] = i + n;
+ qp->upoly = expand(qp->upoly, exp, g_pos);
+ free(exp);
+ if (!qp->upoly)
+ goto error;
+ }
+
+ qp->dim = isl_dim_insert(qp->dim, type, first, n);
+ if (!qp->dim)
+ goto error;
+
+ return qp;
+error:
+ isl_qpolynomial_free(qp);
+ return NULL;
+}
+
+__isl_give isl_qpolynomial *isl_qpolynomial_add_dims(
+ __isl_take isl_qpolynomial *qp, enum isl_dim_type type, unsigned n)
+{
+ unsigned pos;
+
+ pos = isl_qpolynomial_dim(qp, type);
+
+ return isl_qpolynomial_insert_dims(qp, type, pos, n);
+}
+
+__isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_dims(
+ __isl_take isl_pw_qpolynomial *pwqp,
+ enum isl_dim_type type, unsigned n)
+{
+ unsigned pos;
+
+ pos = isl_pw_qpolynomial_dim(pwqp, type);
+
+ return isl_pw_qpolynomial_insert_dims(pwqp, type, pos, n);
+}
+
+static int *reordering_move(isl_ctx *ctx,
+ unsigned len, unsigned dst, unsigned src, unsigned n)
+{
+ int i;
+ int *reordering;
+
+ reordering = isl_alloc_array(ctx, int, len);
+ if (!reordering)
+ return NULL;
+
+ if (dst <= src) {
+ for (i = 0; i < dst; ++i)
+ reordering[i] = i;
+ for (i = 0; i < n; ++i)
+ reordering[src + i] = dst + i;
+ for (i = 0; i < src - dst; ++i)
+ reordering[dst + i] = dst + n + i;
+ for (i = 0; i < len - src - n; ++i)
+ reordering[src + n + i] = src + n + i;
+ } else {
+ for (i = 0; i < src; ++i)
+ reordering[i] = i;
+ for (i = 0; i < n; ++i)
+ reordering[src + i] = dst + i;
+ for (i = 0; i < dst - src; ++i)
+ reordering[src + n + i] = src + i;
+ for (i = 0; i < len - dst - n; ++i)
+ reordering[dst + n + i] = dst + n + i;
+ }
+
+ return reordering;
+}
+
+__isl_give isl_qpolynomial *isl_qpolynomial_move_dims(
+ __isl_take isl_qpolynomial *qp,
+ enum isl_dim_type dst_type, unsigned dst_pos,
+ enum isl_dim_type src_type, unsigned src_pos, unsigned n)
+{
+ unsigned g_dst_pos;
+ unsigned g_src_pos;
+ int *reordering;
+
+ qp = isl_qpolynomial_cow(qp);
+ if (!qp)
+ return NULL;
+
+ isl_assert(qp->dim->ctx, src_pos + n <= isl_dim_size(qp->dim, src_type),
+ goto error);
+
+ g_dst_pos = pos(qp->dim, dst_type) + dst_pos;
+ g_src_pos = pos(qp->dim, src_type) + src_pos;
+ if (dst_type > src_type)
+ g_dst_pos -= n;
+
+ qp->div = isl_mat_move_cols(qp->div, 2 + g_dst_pos, 2 + g_src_pos, n);
+ if (!qp->div)
+ goto error;
+ qp = sort_divs(qp);
+ if (!qp)
+ goto error;
+
+ reordering = reordering_move(qp->dim->ctx,
+ qp->div->n_col - 2, g_dst_pos, g_src_pos, n);
+ if (!reordering)
+ goto error;
+
+ qp->upoly = reorder(qp->upoly, reordering);
+ free(reordering);
+ if (!qp->upoly)
+ goto error;
+
+ qp->dim = isl_dim_move(qp->dim, dst_type, dst_pos, src_type, src_pos, n);
+ if (!qp->dim)
+ goto error;
+
+ return qp;
+error:
+ isl_qpolynomial_free(qp);
+ return NULL;
+}
+
+__isl_give isl_qpolynomial *isl_qpolynomial_from_affine(__isl_take isl_dim *dim,
+ isl_int *f, isl_int denom)
+{
+ struct isl_upoly *up;
+
+ if (!dim)
+ return NULL;
+
+ up = isl_upoly_from_affine(dim->ctx, f, denom, 1 + isl_dim_total(dim));
+
+ return isl_qpolynomial_alloc(dim, 0, up);
+}
+
+__isl_give isl_qpolynomial *isl_qpolynomial_from_constraint(
+ __isl_take isl_constraint *c, enum isl_dim_type type, unsigned pos)
+{
+ isl_int denom;
+ isl_dim *dim;
+ struct isl_upoly *up;
+ isl_qpolynomial *qp;
+ int sgn;
+
+ if (!c)
+ return NULL;
+
+ isl_int_init(denom);
+
+ isl_constraint_get_coefficient(c, type, pos, &denom);
+ isl_constraint_set_coefficient(c, type, pos, c->ctx->zero);
+ sgn = isl_int_sgn(denom);
+ isl_int_abs(denom, denom);
+ up = isl_upoly_from_affine(c->ctx, c->line[0], denom,
+ 1 + isl_constraint_dim(c, isl_dim_all));
+ if (sgn < 0)
+ isl_int_neg(denom, denom);
+ isl_constraint_set_coefficient(c, type, pos, denom);
+
+ dim = isl_dim_copy(c->bmap->dim);
+
+ isl_int_clear(denom);
+ isl_constraint_free(c);
+
+ qp = isl_qpolynomial_alloc(dim, 0, up);
+ if (sgn > 0)
+ qp = isl_qpolynomial_neg(qp);
+ return qp;
+}
+
+/* For each 0 <= i < "n", replace variable "first" + i of type "type"
+ * in "qp" by subs[i].
+ */
+__isl_give isl_qpolynomial *isl_qpolynomial_substitute(
+ __isl_take isl_qpolynomial *qp,
+ enum isl_dim_type type, unsigned first, unsigned n,
+ __isl_keep isl_qpolynomial **subs)
+{
+ int i;
+ struct isl_upoly **ups;
+
+ if (n == 0)
+ return qp;
+
+ qp = isl_qpolynomial_cow(qp);
+ if (!qp)
+ return NULL;
+ for (i = 0; i < n; ++i)
+ if (!subs[i])
+ goto error;
+
+ isl_assert(qp->dim->ctx, first + n <= isl_dim_size(qp->dim, type),
+ goto error);
+
+ for (i = 0; i < n; ++i)
+ isl_assert(qp->dim->ctx, isl_dim_equal(qp->dim, subs[i]->dim),
+ goto error);
+
+ isl_assert(qp->dim->ctx, qp->div->n_row == 0, goto error);
+ for (i = 0; i < n; ++i)
+ isl_assert(qp->dim->ctx, subs[i]->div->n_row == 0, goto error);
+
+ first += pos(qp->dim, type);
+
+ ups = isl_alloc_array(qp->dim->ctx, struct isl_upoly *, n);
+ if (!ups)
+ goto error;
+ for (i = 0; i < n; ++i)
+ ups[i] = subs[i]->upoly;
+
+ qp->upoly = isl_upoly_subs(qp->upoly, first, n, ups);
+
+ free(ups);
+
+ if (!qp->upoly)
+ goto error;
+
+ return qp;
+error:
+ isl_qpolynomial_free(qp);
+ return NULL;
+}
+
+/* Extend "bset" with extra set dimensions for each integer division
+ * in "qp" and then call "fn" with the extended bset and the polynomial
+ * that results from replacing each of the integer divisions by the
+ * corresponding extra set dimension.
+ */
+int isl_qpolynomial_as_polynomial_on_domain(__isl_keep isl_qpolynomial *qp,
+ __isl_keep isl_basic_set *bset,
+ int (*fn)(__isl_take isl_basic_set *bset,
+ __isl_take isl_qpolynomial *poly, void *user), void *user)
+{
+ isl_dim *dim;
+ isl_mat *div;
+ isl_qpolynomial *poly;
+
+ if (!qp || !bset)
+ goto error;
+ if (qp->div->n_row == 0)
+ return fn(isl_basic_set_copy(bset), isl_qpolynomial_copy(qp),
+ user);
+
+ div = isl_mat_copy(qp->div);
+ dim = isl_dim_copy(qp->dim);
+ dim = isl_dim_add(dim, isl_dim_set, qp->div->n_row);
+ poly = isl_qpolynomial_alloc(dim, 0, isl_upoly_copy(qp->upoly));
+ bset = isl_basic_set_copy(bset);
+ bset = isl_basic_set_add(bset, isl_dim_set, qp->div->n_row);
+ bset = add_div_constraints(bset, div);
+
+ return fn(bset, poly, user);
+error:
+ return -1;
+}
+
+/* Return total degree in variables first (inclusive) up to last (exclusive).
+ */
+int isl_upoly_degree(__isl_keep struct isl_upoly *up, int first, int last)
+{
+ int deg = -1;
+ int i;
+ struct isl_upoly_rec *rec;
+
+ if (!up)
+ return -2;
+ if (isl_upoly_is_zero(up))
+ return -1;
+ if (isl_upoly_is_cst(up) || up->var < first)
+ return 0;
+
+ rec = isl_upoly_as_rec(up);
+ if (!rec)
+ return -2;
+
+ for (i = 0; i < rec->n; ++i) {
+ int d;
+
+ if (isl_upoly_is_zero(rec->p[i]))
+ continue;
+ d = isl_upoly_degree(rec->p[i], first, last);
+ if (up->var < last)
+ d += i;
+ if (d > deg)
+ deg = d;
+ }
+
+ return deg;
+}
+
+/* Return total degree in set variables.
+ */
+int isl_qpolynomial_degree(__isl_keep isl_qpolynomial *poly)
+{
+ unsigned ovar;
+ unsigned nvar;
+
+ if (!poly)
+ return -2;
+
+ ovar = isl_dim_offset(poly->dim, isl_dim_set);
+ nvar = isl_dim_size(poly->dim, isl_dim_set);
+ return isl_upoly_degree(poly->upoly, ovar, ovar + nvar);
+}
+
+__isl_give struct isl_upoly *isl_upoly_coeff(__isl_keep struct isl_upoly *up,
+ unsigned pos, int deg)
+{
+ int i;
+ struct isl_upoly_rec *rec;
+
+ if (!up)
+ return NULL;
+
+ if (isl_upoly_is_cst(up) || up->var < pos) {
+ if (deg == 0)
+ return isl_upoly_copy(up);
+ else
+ return isl_upoly_zero(up->ctx);
+ }
+
+ rec = isl_upoly_as_rec(up);
+ if (!rec)
+ return NULL;
+
+ if (up->var == pos) {
+ if (deg < rec->n)
+ return isl_upoly_copy(rec->p[deg]);
+ else
+ return isl_upoly_zero(up->ctx);
+ }
+
+ up = isl_upoly_copy(up);
+ up = isl_upoly_cow(up);
+ rec = isl_upoly_as_rec(up);
+ if (!rec)
+ goto error;
+
+ for (i = 0; i < rec->n; ++i) {
+ struct isl_upoly *t;
+ t = isl_upoly_coeff(rec->p[i], pos, deg);
+ if (!t)
+ goto error;
+ isl_upoly_free(rec->p[i]);
+ rec->p[i] = t;
+ }
+
+ return up;
+error:
+ isl_upoly_free(up);
+ return NULL;
+}
+
+/* Return coefficient of power "deg" of variable "t_pos" of type "type".
+ */
+__isl_give isl_qpolynomial *isl_qpolynomial_coeff(
+ __isl_keep isl_qpolynomial *qp,
+ enum isl_dim_type type, unsigned t_pos, int deg)
+{
+ unsigned g_pos;
+ struct isl_upoly *up;
+ isl_qpolynomial *c;
+
+ if (!qp)
+ return NULL;
+
+ isl_assert(qp->div->ctx, t_pos < isl_dim_size(qp->dim, type),
+ return NULL);
+
+ g_pos = pos(qp->dim, type) + t_pos;
+ up = isl_upoly_coeff(qp->upoly, g_pos, deg);
+
+ c = isl_qpolynomial_alloc(isl_dim_copy(qp->dim), qp->div->n_row, up);
+ if (!c)
+ return NULL;
+ isl_mat_free(c->div);
+ c->div = isl_mat_copy(qp->div);
+ if (!c->div)
+ goto error;
+ return c;
+error:
+ isl_qpolynomial_free(c);
+ return NULL;
+}
+
+/* Homogenize the polynomial in the variables first (inclusive) up to
+ * last (exclusive) by inserting powers of variable first.
+ * Variable first is assumed not to appear in the input.
+ */
+__isl_give struct isl_upoly *isl_upoly_homogenize(
+ __isl_take struct isl_upoly *up, int deg, int target,
+ int first, int last)
+{
+ int i;
+ struct isl_upoly_rec *rec;
+
+ if (!up)
+ return NULL;
+ if (isl_upoly_is_zero(up))
+ return up;
+ if (deg == target)
+ return up;
+ if (isl_upoly_is_cst(up) || up->var < first) {
+ struct isl_upoly *hom;
+
+ hom = isl_upoly_pow(up->ctx, first, target - deg);
+ if (!hom)
+ goto error;
+ rec = isl_upoly_as_rec(hom);
+ rec->p[target - deg] = isl_upoly_mul(rec->p[target - deg], up);
+
+ return hom;
+ }
+
+ up = isl_upoly_cow(up);
+ rec = isl_upoly_as_rec(up);
+ if (!rec)
+ goto error;
+
+ for (i = 0; i < rec->n; ++i) {
+ if (isl_upoly_is_zero(rec->p[i]))
+ continue;
+ rec->p[i] = isl_upoly_homogenize(rec->p[i],
+ up->var < last ? deg + i : i, target,
+ first, last);
+ if (!rec->p[i])
+ goto error;
+ }
+
+ return up;
+error:
+ isl_upoly_free(up);
+ return NULL;
+}
+
+/* Homogenize the polynomial in the set variables by introducing
+ * powers of an extra set variable at position 0.
+ */
+__isl_give isl_qpolynomial *isl_qpolynomial_homogenize(
+ __isl_take isl_qpolynomial *poly)
+{
+ unsigned ovar;
+ unsigned nvar;
+ int deg = isl_qpolynomial_degree(poly);
+
+ if (deg < -1)
+ goto error;
+
+ poly = isl_qpolynomial_insert_dims(poly, isl_dim_set, 0, 1);
+ poly = isl_qpolynomial_cow(poly);
+ if (!poly)
+ goto error;
+
+ ovar = isl_dim_offset(poly->dim, isl_dim_set);
+ nvar = isl_dim_size(poly->dim, isl_dim_set);
+ poly->upoly = isl_upoly_homogenize(poly->upoly, 0, deg,
+ ovar, ovar + nvar);
+ if (!poly->upoly)
+ goto error;
+
+ return poly;
+error:
+ isl_qpolynomial_free(poly);
+ return NULL;
+}
+
+__isl_give isl_term *isl_term_alloc(__isl_take isl_dim *dim,
+ __isl_take isl_mat *div)
+{