Merge branch 'gmp_integration' of necada:~/repo/qpms into gmp_integration

Former-commit-id: 7d6118efbb06d1cee0eb3e89afc4aeb65665d023

qpms/polynomials.c

@@ -325,3 +325,30 @@ void qpq_deriv(qpq_t *dp, const qpq_t *p) {
   dp->order = p->order - 1;
   dp->offset = p->offset - 1 + !p->offset;
 }
+
+
+void qpq_legendroid_init(qpq_legendroid_t *p) {
+  qpq_init(&p->p);
+  p->f = 0;
+}
+
+void qpq_legendroid_clear(qpq_legendroid_t *p) {
+  qpq_clear(&p->p);
+  p->f = 0;
+}
+
+void qpq_legendroid_mul(qpq_legendroid_t *p, const qpq_legendroid_t *a, const qpq_legendroid_t *b) {
+  qpq_mul(&p->p, &a->p, &b->p);
+  if (a->f && b->f) {
+    // TODO make somehow a static representation of this constant polynomial
+    qpq_t ff;
+    qpq_init(&ff);
+    qpq_extend(&ff, 3);
+    qpq_set_elem_si(&ff, 0, -1, 1);
+    qpq_set_elem_si(&ff, 2, 1, 1);
+    qpq_mul(p, &ff);
+    qpq_clear(&ff);
+  }
+  p->f = !(a->f) != !(b->f);
+}
+

qpms/polynomials.h

@@ -71,6 +71,21 @@ void qpq_deriv(qpq_t *dPdx, const qpq_t *P);
 /// Tests whether a polynomial is non-zero.
 _Bool qpq_nonzero(const qpq_t *);
 
+/// A type representing a polynomial with rational coefficients times an optional factor \f$ \sqrt{1-x^2} \f$.
+typedef struct qpq_legendroid_t {
+	qpq_t p;
+	_Bool f;
+} qpq_legendroid_t;
+
+void qpq_legendroid_init(qpq_legendroid_t *p);
+void qpq_legendroid_clear(qpq_legendroid_t *p);
+
+/// Polynomial multiplication.
+void qpq_legendroid_mul(qpq_legendroid_t *product, const qpq_legendroid_t *multiplier, const qpq_legendroid_t *multiplicand);
+
+/// Polynomial derivative.
+void qpq_legendroid_deriv(qpq_legendroid_t *dP_dx, const qpq_legendroid_t *P);
+
 
 /// Polynomial with double coeffs.
 typedef struct qpz_t {