get rid of sage_eval in cfinite_sequence

src/sage/rings/cfinite_sequence.py

@@ -90,6 +90,7 @@
 from numbers import Integral
 
 from sage.categories.rings import Rings
+from sage.libs.pari import pari
 from sage.misc.inherit_comparison import InheritComparisonClasscallMetaclass
 from sage.rings.integer_ring import ZZ
 from sage.rings.rational_field import QQ
@@ -102,11 +103,6 @@
 from sage.structure.parent import Parent
 from sage.structure.unique_representation import UniqueRepresentation
 
-from sage.interfaces.gp import Gp
-from sage.misc.sage_eval import sage_eval
-
-_gp = None
-
 
 def CFiniteSequences(base_ring, names=None, category=None):
     r"""
@@ -1204,6 +1200,13 @@ def guess(self, sequence, algorithm='sage'):
             C-finite sequence, generated by -1/2/(x - 1/2)
             sage: r[0:5]
             [1, 2, 4, 8, 16]
+
+        Using pari::
+
+            sage: r = C.guess([1, 1, 1, 2, 2, 3, 4, 5, 7, 9, 12, 16, 21, 28], algorithm='pari'); r
+            C-finite sequence, generated by (-x - 1)/(x^3 + x^2 - 1)
+            sage: r[0:5]
+            [1, 1, 1, 2, 2]
         """
         S = self.polynomial_ring()
 
@@ -1221,22 +1224,18 @@ def guess(self, sequence, algorithm='sage'):
             return CFiniteSequence(numerator / denominator)
 
         if algorithm == 'pari':
-            global _gp
             if len(sequence) < 6:
                 raise ValueError('sequence too short for guessing')
-            if _gp is None:
-                _gp = Gp()
-                _gp("ggf(v)=local(l,m,p,q,B);l=length(v);B=floor(l/2);\
+            pari("ggf(v)=local(l,m,p,q,B);l=length(v);B=l\\2;\
                 if(B<3,return(0));m=matrix(B,B,x,y,v[x-y+B+1]);\
                 q=qflll(m,4)[1];if(length(q)==0,return(0));\
                 p=sum(k=1,B,x^(k-1)*q[k,1]);\
                 q=Pol(Pol(vector(l,n,v[l-n+1]))*p+O(x^(B+1)));\
                 if(polcoeff(p,0)<0,q=-q;p=-p);q=q/p;p=Ser(q+O(x^(l+1)));\
                 for(m=1,l,if(polcoeff(p,m-1)!=v[m],return(0)));q")
-            _gp.set('gf', sequence)
-            _gp("gf=ggf(gf)")
-            num = S(sage_eval(_gp.eval("Vec(numerator(gf))"))[::-1])
-            den = S(sage_eval(_gp.eval("Vec(denominator(gf))"))[::-1])
+            pari_guess = pari("ggf")(sequence)
+            num = S(pari_guess.numerator().Vec().sage()[::-1])
+            den = S(pari_guess.denominator().Vec().sage()[::-1])
             if num == 0:
                 return 0
             return CFiniteSequence(num / den)