Applying pull-request by d-torrance:

---
Macaulay2 uses givaro as a dependency. However, it builds its own patched
givaro, adding an additional version of the function GFqDom [1]. It would
great if this function existed natively so that Macaulay2 could be built
using a pre-existing givaro on the user's system.
---

Author: jgdumas

examples/Polynomial/Makefile.am

@@ -30,12 +30,13 @@ LDADD = -L${top_srcdir}/src -L${top_srcdir}/src/.libs -lgivaro $(GMP_LIBS) $(LDF
 AM_LDFLAGS=-static
 
 
-EXTRA_PROGRAMS=isirred isprimitive trunc_arith pol_arith pol_eval pol_factor interpolate PolynomialCRT highorder bivariate
+EXTRA_PROGRAMS=isirred isprimitive trunc_arith pol_arith pol_eval pol_factor interpolate PolynomialCRT highorder bivariate isgenerator
 
 CLEANFILES=$(EXTRA_PROGRAMS)
 
 interpolate_SOURCES   = interpolate.C
 isirred_SOURCES       = isirred.C
+isgenerator_SOURCES       = isgenerator.C
 isprimitive_SOURCES   = isprimitive.C
 pol_arith_SOURCES     = pol_arith.C
 trunc_arith_SOURCES   = trunc_arith.C

examples/Polynomial/isgenerator.C

@@ -0,0 +1,53 @@
+// Copyright(c)'1994-2009 by The Givaro group
+// This file is part of Givaro.
+// Givaro is governed by the CeCILL-B license under French law
+// and abiding by the rules of distribution of free software.
+// see the COPYRIGHT file for more details.
+/*! @file examples/Polynomial/isprimitive.C
+ * @ingroup examples
+ * @ingroup polynomials
+ * @example examples/Polynomial/isprimitive.C
+ * @brief NO DOC
+ */
+
+#include <iostream>
+#include <stdlib.h>
+#include <givaro/gfq.h>
+#include <givaro/givpoly1factor.h>
+#include <givaro/givtimer.h>
+
+// using namespace std;
+
+using namespace Givaro;
+
+
+int main(int argc, char** argv)
+{
+    typedef GFqDom<int64_t>::Residu_t UT;
+    UT MOD;
+    if (argc > 1)
+        MOD = (UT)atoi(argv[1]);
+    else
+        std::cin >> MOD;
+    uint64_t expo = 1;
+    if (argc > 2) expo = (uint64_t)atoi(argv[2]);
+    
+    GFqDom<int64_t> F(MOD, expo);
+    
+    Poly1FactorDom<GFqDom<int64_t>, Dense> FD(F,Indeter("X"));
+    Poly1FactorDom<GFqDom<int64_t>, Dense>::Element P, G;
+    FD.read( std::cin, P );
+    FD.read( std::cin, G );
+    
+    Timer tim; tim.clear(); tim.start();
+    bool f = FD.is_prim_root(G, P );
+    tim.stop();
+    
+    FD.write(F.write( FD.write( std::cout, G ) << " is " << (f?"":"not ") << " a generator in " ) << " defined with ", P) << std::endl;
+    
+        // std::cout << f << std::endl;
+    std::cerr << tim << std::endl;
+    
+    return 0;
+}
+

src/kernel/field/gfq.h

@@ -5,7 +5,7 @@
 // and abiding by the rules of distribution of free software.
 // see the COPYRIGHT file for more details.
 // file: gfq.h
-// Time-stamp: <28 Oct 15 20:48:41 Jean-Guillaume.Dumas@imag.fr>
+// Time-stamp: <17 Jul 16 16:12:52 Jean-Guillaume.Dumas@imag.fr>
 // date: 1999
 // version:
 // author: Jean-Guillaume.Dumas
@@ -98,6 +98,14 @@ template<class TT> class GFqDom {
     template<typename Vector>
     GFqDom(const UTT P, const UTT e, const Vector& modPoly);
 
+        // Construction with prescribed irreducible polynomial
+        //   and with prescribed generator polynomial
+        //   coefficients of the vector should be integers-like
+        //   there will be a call to this->init to build the
+        //   representation of both polynomials
+    template<typename Vector>
+    GFqDom( const UTT P, const UTT e, const Vector& modPoly, const Vector& genPoly);
+
     GFqDom( const GFqDom<TT>& F)
             : zero(F.zero),
               one(F.one),

src/kernel/field/gfq.inl

@@ -1115,6 +1115,77 @@ namespace Givaro {
         _plus1[size_t(mOne)] = 0;
     }
 
+         // Construction with prescribed irreducible polynomial
+        //   and with prescribed generator polynomial
+        //   coefficients of the vector should be integers-like
+        //   there will be a call to this->init to build the
+        //   representation of both polynomials
+    template<typename TT>
+    template<typename Vector>
+    inline GFqDom<TT>::GFqDom(const UTT P, const UTT e, 
+                              const Vector& modPoly, const Vector& genPoly):
+            zero(0)
+        , one ((TT) power(P,e) - 1  )
+        , mOne(  (P==2)?  (one)  :  ( one >> 1) )   // 1 == -1 in GF(2^k)
+        , _characteristic(P)
+        , _exponent(e)
+        , _q( (UTT) one + 1 )
+        , _qm1 ( (UTT)one )
+        , _log2pol( (UT)_q )
+        , _pol2log( (UT)_q )
+        , _plus1( (UT)_q )
+        , _dcharacteristic( (double)P )
+    {
+
+            // 1 is represented by q-1, zero by 0
+        _log2pol[0] = (UTT)zero;
+
+        GFqDom<TT> Zp(P,1);
+        typedef Poly1FactorDom< GFqDom<TT>, Dense > PolDom;
+        PolDom Pdom( Zp );
+        typename PolDom::Element Ft, F(e+1), G(genPoly.size()), H;
+
+        for( size_t i = 0; i < F.size(); ++i )
+            Zp.init( F[i], modPoly[i]);
+
+        for( size_t i = 0; i < G.size(); ++i )
+            Zp.init( G[i], genPoly[i]);
+
+        Pdom.assign(H,G);
+
+        typedef Poly1PadicDom< GFqDom<TT>, Dense > PadicDom;
+        PadicDom PAD(Pdom);
+
+        PAD.eval(_log2pol[1],H);
+        PAD.eval(_irred, F);
+
+        for (UTT i = 2; i < _qm1; ++i) {
+            Pdom.mulin(H, G);
+            Pdom.modin(H, F);
+            PAD.eval(_log2pol[i], H);
+        }
+        _log2pol[_qm1] = 1;
+
+        _log2pol[0] = 0;
+
+        for (UTT i = 0; i < _q; ++i)
+            _pol2log[ _log2pol[i] ] = i;
+
+        _plus1[0] = 0;
+
+        UTT a,b,r;
+        for (UTT i = 1; i < _q; ++i) {
+            a = _log2pol[i];
+            r = a % P;
+            if (r == (P - 1))
+                b = a - r;
+            else
+                b = a + 1;
+            _plus1[i] = (TT)_pol2log[b] - (TT)_qm1;
+        }
+
+        _plus1[size_t(mOne)] = 0;
+    }
 
     template<typename TT> inline void GFqDom<TT>::Init() {}
 

tests/test-ffarith.C

@@ -371,12 +371,19 @@ int main(int argc, char ** argv)
 
     // Zech log finite field with 256 elements
     // and prescribed 1 + x +x^3 +x^4 +x^8 irreducible polynomial
-    std::vector< GFqDom<int64_t>::Residu_t > Irred(9);
-    Irred[0] = 1; Irred[1] = 1; Irred[2] = 0; Irred[3] = 1;
-    Irred[4] = 1; Irred[5] = 0; Irred[6] = 0; Irred[7] = 0;
-    Irred[8] = 1;
+//     std::vector< GFqDom<int64_t>::Residu_t > Irred(9);
+//     Irred[0] = 1; Irred[1] = 1; Irred[2] = 0; Irred[3] = 1;
+//     Irred[4] = 1; Irred[5] = 0; Irred[6] = 0; Irred[7] = 0;
+//     Irred[8] = 1;
+    std::vector< int64_t > Irred {1,1,0,1,1,0,0,0,1};
     TEST_SPECIFIC(GFqDom<int64_t>, GF256, 2, 8, Irred);
 
+   // Zech log finite field with 343 elements
+   // and prescribed 3 +x^3  irreducible polynomial
+   // and prescribed 5 +3x +4x^2 generator polynomial
+    std::vector< int64_t > Irred3 {3,0,0,1}, Gene3 {5,3,4};
+    TEST_SPECIFIC(GFqDom<int64_t>, GF343, 7, 3, Irred3, Gene3);
+
     TEST_SPECIFIC(GFqDom<int32_t>, GF625, 5, 4);
     TEST_SPECIFIC(GFqExt<int32_t>, GF81, 3, 4);