Renamed files *.tcc and *.hpp to *.h.

[ginac.git] / ginac / polynomial / remainder.h

diff --git a/ginac/polynomial/remainder.h b/ginac/polynomial/remainder.h
new file mode 100644 (file)
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--- /dev/null
+++ b/ginac/polynomial/remainder.h
@@ -0,0 +1,116 @@
+#ifndef GINAC_UPOLY_REMAINDER_TCC
+#define GINAC_UPOLY_REMAINDER_TCC
+#include "upoly.h"
+#include "ring_traits.h"
+#include "upoly_io.h"
+#include "debug.h"
+
+namespace GiNaC
+{
+/**
+ * @brief Polynomial remainder for univariate polynomials over fields
+ *
+ * Given two univariate polynomials \f$a, b \in F[x]\f$, where F is
+ * a finite field (presumably Z/p) computes the remainder @a r, which is
+ * defined as \f$a = b q + r\f$. Returns true if the remainder is zero
+ * and false otherwise.
+ */
+static bool
+remainder_in_field(umodpoly& r, const umodpoly& a, const umodpoly& b)
+{
+       typedef cln::cl_MI field_t;
+
+       if (degree(a) < degree(b)) {
+               r = a;
+               return false;
+       }
+       // The coefficient ring is a field, so any 0 degree polynomial
+       // divides any other polynomial.
+       if (degree(b) == 0) {
+               r.clear();
+               return true;
+       }
+
+       r = a;
+       const field_t b_lcoeff = lcoeff(b);
+       for (std::size_t k = a.size(); k-- >= b.size(); ) {
+
+               // r -= r_k/b_n x^{k - n} b(x)
+               if (zerop(r[k]))
+                       continue;
+
+               field_t qk = div(r[k], b_lcoeff);
+               bug_on(zerop(qk), "division in a field yield zero: "
+                                  << r[k] << '/' << b_lcoeff);
+
+               // Why C++ is so off-by-one prone?
+               for (std::size_t j = k, i = b.size(); i-- != 0; --j) {
+                       if (zerop(b[i]))
+                               continue;
+                       r[j] = r[j] - qk*b[i];
+               }
+               bug_on(!zerop(r[k]), "polynomial division in field failed: " <<
+                                     "r[" << k << "] = " << r[k] << ", " <<
+                                     "r = " << r << ", b = " << b);
+
+       }
+
+       // Canonicalize the remainder: remove leading zeros. Give a hint
+       // to canonicalize(): we know degree(remainder) < degree(b) 
+       // (because the coefficient ring is a field), so 
+       // c_{degree(b)} \ldots c_{degree(a)} are definitely zero.
+       std::size_t from = degree(b) - 1;
+       canonicalize(r, from);
+       return r.empty();
+}
+
+/**
+ * @brief Polynomial remainder for univariate polynomials over a ring. 
+ *
+ * Given two univariate polynomials \f$a, b \in R[x]\f$, where R is
+ * a ring (presumably Z) computes the remainder @a r, which is
+ * defined as \f$a = b q + r\f$. Returns true if the remainder is zero
+ * and false otherwise.
+ */
+template<typename T>
+bool remainder_in_ring(T& r, const T& a, const T& b)
+{
+       typedef typename T::value_type ring_t;
+       if (degree(a) < degree(b)) {
+               r = a;
+               return false;
+       }
+       // N.B: don't bother to optimize division by constant
+
+       r = a;
+       const ring_t b_lcoeff = lcoeff(b);
+       for (std::size_t k = a.size(); k-- >= b.size(); ) {
+
+               // r -= r_k/b_n x^{k - n} b(x)
+               if (zerop(r[k]))
+                       continue;
+
+               const ring_t qk = truncate1(r[k], b_lcoeff);
+
+               // Why C++ is so off-by-one prone?
+               for (std::size_t j = k, i = b.size(); i-- != 0; --j) {
+                       if (zerop(b[i]))
+                               continue;
+                       r[j] = r[j] - qk*b[i];
+               }
+
+               if (!zerop(r[k])) {
+                       // division failed, don't bother to continue
+                       break;
+               }
+       }
+
+       // Canonicalize the remainder: remove leading zeros. We can't say
+       // anything about the degree of the remainder here.
+       canonicalize(r);
+       return r.empty();
+}
+} // namespace GiNaC
+
+#endif // GINAC_UPOLY_REMAINDER_TCC
+