Ticket #8909: 8909_gap2cyclotomic.patch

sage/groups/matrix_gps/matrix_group.py

@@ -17 +17 @@
   to GAP's MeatAxe implementation) and as_permutation_group (returns
   isomorphic PermutationGroup).
 
+- Simon King (2010-05): Improve invariant_generators by using GAP
+  for the construction of the Reynolds operator in Singular.
+
 This class is designed for computing with matrix groups defined by
 a (relatively small) finite set of generating matrices.
 
@@ -1056 +1059 @@
         from sage.interfaces.singular import singular
         gens = self.gens()
         singular.LIB("finvar.lib")
-        n = len((gens[0].matrix()).rows())
+        n = self.degree() #len((gens[0].matrix()).rows())
         F = self.base_ring()
         q = F.characteristic()
         ## test if the field is admissible
@@ -1083 +1086 @@
         Lgens = ','.join((x.name() for x in A))
         PR = PolynomialRing(F,n,[VarStr+str(i) for i in range(1,n+1)])
         if q == 0 or (q > 0 and self.cardinality()%q != 0):
-            ReyName = 't'+singular._next_var_name()
-            singular.eval('list %s=group_reynolds((%s))'%(ReyName,Lgens))
-            IRName = 't'+singular._next_var_name()
-            singular.eval('matrix %s = invariant_algebra_reynolds(%s[1])'%(IRName,ReyName))
+            from sage.all import Integer, Matrix
+            try:
+                gapself = gap(self)
+                # test whether the backwards transformation works as well:
+                for i in range(self.ngens()):
+                    if Matrix(gapself.gen(i+1),F) != self.gen(i).matrix():
+                        raise ValueError
+            except (TypeError,ValueError):
+                gapself is None
+            if gapself is not None:
+                ReyName = 't'+singular._next_var_name()
+                singular.eval('matrix %s[%d][%d]'%(ReyName,self.cardinality(),n))
+                En = gapself.Enumerator()
+                for i in range(1,self.cardinality()+1):
+                    M = Matrix(En[i],F)
+                    D = [{} for foobar in range(self.degree())]
+                    for x,y in M.dict().items():
+                        D[x[0]][x[1]] = y
+                    for row in range(self.degree()):
+                        for t in D[row].items():
+                            singular.eval('%s[%d,%d]=%s[%d,%d]+(%s)*var(%d)'%(ReyName,i,row+1,ReyName,i,row+1, repr(t[1]),t[0]+1))
+                foobar = singular(ReyName)
+                IRName = 't'+singular._next_var_name()
+                singular.eval('matrix %s = invariant_algebra_reynolds(%s)'%(IRName,ReyName))
+            else:
+                ReyName = 't'+singular._next_var_name()
+                singular.eval('list %s=group_reynolds((%s))'%(ReyName,Lgens))
+                IRName = 't'+singular._next_var_name()
+                singular.eval('matrix %s = invariant_algebra_reynolds(%s[1])'%(IRName,ReyName))
+
             OUT = [singular.eval(IRName+'[1,%d]'%(j)) for j in range(1,1+singular('ncols('+IRName+')'))]
             return [PR(gen) for gen in OUT]
         if self.cardinality()%q == 0:

sage/rings/number_field/number_field.py

@@ -11 +11 @@
 
 - Robert Bradshaw (2008-10): specified embeddings into ambient fields
 
+- Simon King(2010-05): Improve coercion from GAP
+
 .. note::
 
    Unlike in PARI/GP, class group computations *in Sage* do *not* by default
@@ -6730 +6732 @@
             z^2 + 3
             sage: k5(w)
             z^2 + 3
+
+        It may be that GAP uses a name for the generator of the cyclotomic field.
+        We can deal with this case, if this name coincides with the name in Sage::
+
+            sage: F=CyclotomicField(8)
+            sage: z=F.gen()
+            sage: a=gap(z+1/z); a
+            -zeta8^3+zeta8
+            sage: F(a)
+            -zeta8^3 + zeta8
+
+        In some cases, the string representation in GAP contains an exclamation
+        mark, which used to be a problem in earlier versions of Sage. Now, we can
+        deal with it as well::
+
+            sage: b=gap(Matrix(F,[[z^2,1],[0,a+1]])); b
+            [ [ zeta8^2, !1 ], [ !0, -zeta8^3+zeta8+1 ] ]
+            sage: b[1,2]
+            !1
+            sage: F(b[1,2])
+            1
+            sage: Matrix(b,F)
+            [             zeta8^2                    1]
+            [                   0 -zeta8^3 + zeta8 + 1]
         """
         s = str(x)
         i = s.find('E(')
         if i == -1:
-            return self(rational.Rational(s))
+            try:
+                # it may be that a number field element's string representation
+                # in GAP has an exclamation mark in it.
+                return self(rational.Rational(s.replace('!','')))
+            except:
+                # There is no 'E(...)' in the string representation. But it may
+                # be that 'E(...)' was overwritten in GAP. We can only hope that
+                # by coincidence the name in GAP is the same as the name in self
+                return self._coerce_from_str(s.replace('!',''))
         j = i + s[i:].find(')')
         n = int(s[i+2:j])
         if n == self.zeta_order():
@@ -6742 +6776 @@
         else:
             K = CyclotomicField(n)
         zeta = K.gen()
-        s = s.replace('E(%s)'%n,'zeta')
-        s = sage.misc.all.sage_eval(s, locals={'zeta':K.gen()})
+        zeta_name = K.variable_name()
+        while zeta_name in s: # could be that gap uses the generator name for a different purpose
+            zeta_name = zeta_name+'_'
+        s = s.replace('E(%s)'%n,zeta_name)
+        s = sage.misc.all.sage_eval(s, locals={zeta_name:zeta})
         if K is self:
             return s
         else: