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diff --git a/moon-abe/pbc-0.5.14/include/pbc_ternary_extension_field.h b/moon-abe/pbc-0.5.14/include/pbc_ternary_extension_field.h
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+// some ternary extension fields,
+// including $GF(3^m) = GF(3)[x]/(x^m + x^t + 2)$,
+// $GF(3^{2*m}) = GF(3^m)[x]/(x^2 + 1)$,
+// $GF(3^{3*m}) = GF(3^m)[x]/(x^3 - x - 1)$,
+// and $GF(3^{6*m}) = GF(3^{2*m})[x]/(x^3 - x - 1)$
+//
+// Requires:
+// * pbc_field.h
+
+#ifndef __PBC_TERNARY_EXTENSION_FIELD_H__
+#define __PBC_TERNARY_EXTENSION_FIELD_H__
+
+/* initialize $f$ as $GF(3)[x]/(x^m + x^t + 2)$ */
+void field_init_gf3m(field_t f, unsigned m, unsigned t);
+
+/* initialize $f$ as $base_field[x]/(x^2 + 1)$ */
+void field_init_gf32m(field_t f, field_t base_field);
+
+/* initialize $f$ as $base_field[x]/(x^3 - x - 1)$ */
+void field_init_gf33m(field_t f, field_t base_field);
+
+#endif //__PBC_TERNARY_EXTENSION_FIELD_H__