polys: alter construction of RootOf's with algebraic coefficients

Now we don't canonicalize polynomial coefficients to be integers,
instead expand_func() helper does this job.

diofant/polys/rootoftools.py

@@ -58,7 +58,7 @@ class RootOf(Expr):
     Examples
     ========
 
-    >>> RootOf(x**3 + I*x + 2, 0, extension=True)
+    >>> expand_func(RootOf(x**3 + I*x + 2, 0, extension=True))
     RootOf(x**6 + 4*x**3 + x**2 + 4, 1)
     """
 
@@ -121,22 +121,6 @@ def __new__(cls, f, x, index=None, radicals=True, expand=True,
 
         coeff, poly = preprocess_roots(poly, extension=extension)
 
-        if poly.domain.is_AlgebraicField and extension:
-            if poly.domain.domain.is_AlgebraicField:
-                new_domain = QQ.algebraic_field(poly.domain.domain.ext,
-                                                poly.domain.ext)
-                poly = poly.set_domain(new_domain)
-            x, y = poly.gen, Dummy('y')
-            p = sum(Poly(c.rep, y)*x**n for (n,), c in poly.rep.terms()).inject(x)
-            q = poly.domain.minpoly.eval(y)
-            minpoly = PurePoly(resultant(p, q, y), x)
-            for idx, r in enumerate(minpoly.all_roots()):  # pragma: no branch
-                if poly.as_expr().evalf(2, subs={x: r}, chop=True) == 0:
-                    index -= 1
-                    if index == -1:
-                        break
-            poly, index = minpoly, idx
-
         if poly.domain.is_IntegerRing or poly.domain == QQ.algebraic_field(I):
             root = cls._indexed_root(poly, index)
         else:
@@ -175,6 +159,26 @@ def args(self):
     def free_symbols(self):
         return self.poly.free_symbols
 
+    def _eval_expand_func(self, **hints):
+        poly = self.poly
+        index = self.index
+        if poly.domain.is_AlgebraicField:
+            if poly.domain.domain.is_AlgebraicField:
+                new_domain = QQ.algebraic_field(poly.domain.domain.ext,
+                                                poly.domain.ext)
+                poly = poly.set_domain(new_domain)
+            x, y = poly.gen, Dummy('y')
+            p = sum(Poly(c.rep, y)*x**n for (n,), c in poly.rep.terms()).inject(x)
+            q = poly.domain.minpoly.eval(y)
+            minpoly = PurePoly(resultant(p, q, y), x)
+            for idx, r in enumerate(minpoly.all_roots()):  # pragma: no branch
+                if poly.as_expr().evalf(2, subs={x: r}, chop=True) == 0:
+                    index -= 1
+                    if index == -1:
+                        break
+            poly, index = minpoly, idx
+        return self.func(poly.as_expr(), poly.gen, index)
+
     def _eval_is_real(self):
         try:
             return self.index < len(_reals_cache[self.poly.rep])

diofant/polys/tests/test_rootoftools.py

@@ -3,8 +3,8 @@
 import pytest
 
 from diofant import (Eq, Float, Function, I, Lambda, Pow, Rational, Symbol,
-                     conjugate, exp, false, legendre_poly, log, oo, root,
-                     solve, sqrt, tan, true)
+                     conjugate, exp, expand_func, false, legendre_poly, log,
+                     oo, root, solve, sqrt, tan, true)
 from diofant.abc import a, b, r, x, y, z
 from diofant.polys.polyerrors import (GeneratorsNeeded,
                                       MultivariatePolynomialError,
@@ -543,12 +543,14 @@ def test_rewrite():
 
 
 @pytest.mark.slow
-def test_RootOf_algebraic_domain():
-    assert RootOf(x**3 + I*x + 2, 0,
-                  extension=True) == RootOf(x**6 + 4*x**3 + x**2 + 4, 1)
-    assert RootOf(x**3 + I*x + 2, 1,
-                  extension=True) == RootOf(x**6 + 4*x**3 + x**2 + 4, 3)
+def test_RootOf_expand_func():
+    r0 = RootOf(x**3 + x + 2, 0)
+    assert expand_func(r0) == r0
+    r0 = RootOf(x**3 + I*x + 2, 0, extension=True)
+    assert expand_func(r0) == RootOf(x**6 + 4*x**3 + x**2 + 4, 1)
+    r1 = RootOf(x**3 + I*x + 2, 1, extension=True)
+    assert expand_func(r1) == RootOf(x**6 + 4*x**3 + x**2 + 4, 3)
 
     e = RootOf(x**4 + sqrt(2)*x**3 - I*x + 1, 0, extension=True)
-    assert e == RootOf(x**16 - 4*x**14 + 8*x**12 - 6*x**10 +
-                       10*x**8 + 5*x**4 + 2*x**2 + 1, 1)
+    assert expand_func(e) == RootOf(x**16 - 4*x**14 + 8*x**12 - 6*x**10 +
+                                    10*x**8 + 5*x**4 + 2*x**2 + 1, 1)

docs/release/notes-0.10.rst

@@ -46,6 +46,7 @@ Compatibility breaks
 * Removed ``@public`` decorator, see :pull:`666`.
 * Removed ``dummy_eq()`` method from :class:`~diofant.core.basic.Basic`, see :pull:`666`.
 * :class:`~diofant.core.function.Subs` now support only ``Subs(expr, (var1, val1), (var2, val2), ...)`` syntax, see :pull:`667`.
+* :class:`~diofant.polys.rootoftools.RootOf` don't canonicalize anymore polynomials to have integer coefficients, use :func:`~diofant.core.function.expand_func` instead, see :pull:`679`.
 
 Minor changes
 =============