Merge pull request diofant#732 from skirpichev/misc-poly

Misc poly fixes

diofant/calculus/optimization.py

@@ -140,7 +140,7 @@ def minimize_univariate(f, x, dom):
     elif dom.is_FiniteSet:
         for p in dom.args:
             extr[p] = f.subs({x: p})
-    else:  # pragma: no cover
+    else:
         raise NotImplementedError
 
     if extr:

diofant/calculus/singularities.py

@@ -48,7 +48,7 @@ def singularities(f, x):
     elif f.func in (log, sign) and len(f.args) == 1:
         guess |= singularities(f.args[0], x)
         guess |= {s[x] for s in solve(f.args[0], x) if s[x].is_real}
-    else:  # pragma: no cover
+    else:
         raise NotImplementedError
 
     for s in guess:

diofant/concrete/gosper.py

@@ -101,7 +101,8 @@ def gosper_term(f, n):
     elif not N:
         D = {K - N + 1, Integer(0)}
     else:
-        D = {K - N + 1, (B.nth(N - 1) - A.nth(N - 1))/A.LC()}
+        D = {K - N + 1, (B.coeff_monomial(n**(N - 1)) -
+                         A.coeff_monomial(n**(N - 1)))/A.LC()}
 
     for d in set(D):
         if not d.is_Integer or d < 0:

diofant/concrete/summations.py

@@ -202,7 +202,7 @@ def _eval_derivative(self, x):
             if limit[0] not in df.free_symbols:
                 rv = rv.doit()
             return rv
-        else:  # pragma: no cover
+        else:
             raise NotImplementedError('Lower and upper bound expected.')
 
     def _eval_simplify(self, ratio, measure):

diofant/core/evalf.py

@@ -636,7 +636,7 @@ def evalf_trig(v, prec, options):
         func = mpf_cos
     elif isinstance(v, sin):
         func = mpf_sin
-    else:  # pragma: no cover
+    else:
         raise NotImplementedError
     arg = v.args[0]
     # 20 extra bits is possibly overkill. It does make the need
@@ -652,7 +652,7 @@ def evalf_trig(v, prec, options):
             return fone, None, prec, None
         elif isinstance(v, sin):
             return None, None, None, None
-        else:  # pragma: no cover
+        else:
             raise NotImplementedError
     # For trigonometric functions, we are interested in the
     # fixed-point (absolute) accuracy of the argument.

diofant/core/expr.py

@@ -984,7 +984,6 @@ def coeff(self, x, n=1, right=False):
         diofant.core.expr.Expr.as_coeff_Mul
         diofant.core.expr.Expr.as_independent
         diofant.polys.polytools.Poly.coeff_monomial
-        diofant.polys.polytools.Poly.nth
 
         Examples
         ========
@@ -1298,8 +1297,6 @@ def as_coefficient(self, expr):
         Poly(x*E + 2*E, x, E, domain='ZZ')
         >>> p.coeff_monomial(E)
         2
-        >>> p.nth(0, 1)
-        2
 
         Since the following cannot be written as a product containing
         E as a factor, None is returned. (If the coefficient ``2*x`` is
@@ -1323,7 +1320,6 @@ def as_coefficient(self, expr):
         as_coeff_Mul: separate the multiplicative constant from an expression
         as_independent: separate x-dependent terms/factors from others
         diofant.polys.polytools.Poly.coeff_monomial: efficiently find the single coefficient of a monomial in Poly
-        diofant.polys.polytools.Poly.nth: like coeff_monomial but powers of monomial terms are used
         """
 
         r = self.extract_multiplicatively(expr)
@@ -1806,7 +1802,7 @@ def extract_multiplicatively(self, c):
                     return
                 else:
                     return quotient
-            else:  # pragma: no cover
+            else:
                 raise NotImplementedError
         elif self.is_Add:
             cs, ps = self.primitive()

diofant/core/mul.py

@@ -834,7 +834,7 @@ def _matches(self, expr, repl_dict={}):
             a = self.func(*nc1)
             if not isinstance(a, self.func):
                 repl_dict = a._matches(self.func(*nc2), repl_dict)
-            else:  # pragma: no cover
+            else:
                 raise NotImplementedError
         return repl_dict or None
 

diofant/core/multidimensional.py

@@ -22,7 +22,7 @@ def apply_on_element(f, args, kwargs, n):
     elif isinstance(n, str):
         structure = kwargs[n]
         is_arg = False
-    else:  # pragma: no cover
+    else:
         raise NotImplementedError
 
     # Define reduced function that is only dependend of the specified argument.
@@ -122,7 +122,7 @@ def wrapper(*args, **kwargs):
                     except KeyError:
                         continue
                     is_arg = False
-                else:  # pragma: no cover
+                else:
                     raise NotImplementedError
 
                 if hasattr(entry, "__iter__"):

diofant/core/operations.py

@@ -235,7 +235,7 @@ def _matches_commutative(self, expr, repl_dict={}):
                         i += 0
                         continue
 
-                else:  # pragma: no cover
+                else:
                     raise NotImplementedError
 
                 break  # if we didn't continue, there is nothing more to do

diofant/core/relational.py

@@ -108,7 +108,7 @@ def canonical(self):
             pass
         elif r.func in (Eq, Ne):
             r = r.func(*ordered(r.args), evaluate=False)
-        else:  # pragma: no cover
+        else:
             raise NotImplementedError
         if r.lhs.is_Number and not r.rhs.is_Number:
             r = r.reversed
@@ -208,7 +208,7 @@ def as_set(self):
 
         if len(syms) == 1:
             sym = syms.pop()
-        else:  # pragma: no cover
+        else:
             raise NotImplementedError("Sorry, Relational.as_set procedure"
                                       " is not yet implemented for"
                                       " multivariate expressions")

diofant/functions/elementary/piecewise.py

@@ -240,7 +240,7 @@ def _eval_interval(self, sym, a, b):
                     elif ((b >= lower) is S.true) and ((b <= upper) is S.true):
                         rep = a
                         val = e._eval_interval(sym, a, b)
-                    else:  # pragma: no cover
+                    else:
                         raise NotImplementedError(
                             """The evaluation of a Piecewise interval when both the lower
                             and the upper limit are symbolic is not yet implemented.""")
@@ -326,7 +326,7 @@ def _sort_expr_cond(self, sym, a, b, targetcond=None):
                         upper = Min(cond2.gts, upper)
                     elif cond2.gts == sym:
                         lower = Max(cond2.lts, lower)
-                    else:  # pragma: no cover
+                    else:
                         raise NotImplementedError(
                             "Unable to handle interval evaluation of expression.")
             else:
@@ -335,7 +335,7 @@ def _sort_expr_cond(self, sym, a, b, targetcond=None):
                     lower = -oo   # e.g. x <= 0 ---> -oo <= 0
                 elif cond.gts == sym:            # part 1a: ... that can be expanded
                     upper = oo           # e.g. x >= 0 --->  oo >= 0
-                else:  # pragma: no cover
+                else:
                     raise NotImplementedError(
                         "Unable to handle interval evaluation of expression.")
 

diofant/functions/special/bessel.py

@@ -700,13 +700,13 @@ def spherical_jn(n, x):
 
         def f(x):
             return spherical_jn(n, x)
-    else:  # pragma: no cover
+    else:
         raise NotImplementedError("Unknown method.")
 
     def solver(f, x):
         if method == "scipy":
             root = newton(f, x)
-        else:  # pragma: no cover
+        else:
             raise NotImplementedError("Unknown method.")
         return root
 

diofant/geometry/ellipse.py

@@ -744,7 +744,7 @@ def is_tangent(self, o):
                 inter = self._do_line_intersection(seg)
                 c += len([True for point in inter if point in seg])
             return c == 1
-        else:  # pragma: no cover
+        else:
             raise NotImplementedError("Unknown argument type")
 
     def normal_lines(self, p, prec=None):

diofant/geometry/plane.py

@@ -726,5 +726,5 @@ def is_coplanar(self, o):
             return not cancel(self.equation(x, y, z)/o.equation(x, y, z)).has(x, y, z)
         elif isinstance(o, Point3D):
             return o in self
-        else:  # pragma: no cover
+        else:
             raise NotImplementedError

diofant/geometry/polygon.py

@@ -686,7 +686,7 @@ def distance(self, o):
             return dist
         elif isinstance(o, Polygon) and self.is_convex() and o.is_convex():
             return self._do_poly_distance(o)
-        else:  # pragma: no cover
+        else:
             raise NotImplementedError
 
     def _do_poly_distance(self, e2):

diofant/integrals/prde.py

@@ -183,7 +183,7 @@ def prde_linear_constraints(a, b, G, DE):
 
     if not all(ri.is_zero for _, ri in Q):
         N = max(ri.degree(DE.t) for _, ri in Q)
-        M = Matrix(N + 1, m, lambda i, j: Q[j][1].nth(i))
+        M = Matrix(N + 1, m, lambda i, j: Q[j][1].coeff_monomial((i,)))
     else:
         M = Matrix()  # No constraints, return the empty matrix.
 
@@ -302,7 +302,7 @@ def prde_no_cancel_b_large(b, Q, n, DE):
 
     for N in range(n, -1, -1):  # [n, ..., 0]
         for i in range(m):
-            si = Q[i].nth(N + db)/b.LC()
+            si = Q[i].coeff_monomial((N + db,))/b.LC()
             sitn = Poly(si*DE.t**N, DE.t)
             H[i] = H[i] + sitn
             Q[i] = Q[i] - derivation(sitn, DE) - b*sitn
@@ -312,7 +312,7 @@ def prde_no_cancel_b_large(b, Q, n, DE):
         M = zeros(0, 2)
     else:
         dc = max(qi.degree(DE.t) for qi in Q)
-        M = Matrix(dc + 1, m, lambda i, j: Q[j].nth(i))
+        M = Matrix(dc + 1, m, lambda i, j: Q[j].coeff_monomial((i,)))
     A, u = constant_system(M, zeros(dc + 1, 1), DE)
     c = eye(m)
     A = A.row_join(zeros(A.rows, m)).col_join(c.row_join(-c))
@@ -336,22 +336,22 @@ def prde_no_cancel_b_small(b, Q, n, DE):
 
     for N in range(n, 0, -1):  # [n, ..., 1]
         for i in range(m):
-            si = Q[i].nth(N + DE.d.degree(DE.t) - 1)/(N*DE.d.LC())
+            si = Q[i].coeff_monomial((N + DE.d.degree(DE.t) - 1,))/(N*DE.d.LC())
             sitn = Poly(si*DE.t**N, DE.t)
             H[i] = H[i] + sitn
             Q[i] = Q[i] - derivation(sitn, DE) - b*sitn
 
     if b.degree(DE.t) > 0:
         for i in range(m):
-            si = Poly(Q[i].nth(b.degree(DE.t))/b.LC(), DE.t)
+            si = Poly(Q[i].coeff_monomial((b.degree(DE.t),))/b.LC(), DE.t)
             H[i] = H[i] + si
             Q[i] = Q[i] - derivation(si, DE) - b*si
         if all(qi.is_zero for qi in Q):
             dc = -1
             M = Matrix()
         else:
             dc = max(qi.degree(DE.t) for qi in Q)
-            M = Matrix(dc + 1, m, lambda i, j: Q[j].nth(i))
+            M = Matrix(dc + 1, m, lambda i, j: Q[j].coeff_monomial((i,)))
         A, u = constant_system(M, zeros(dc + 1, 1), DE)
         c = eye(m)
         A = A.row_join(zeros(A.rows, m)).col_join(c.row_join(-c))
@@ -469,7 +469,7 @@ def parametric_log_deriv_heu(fa, fd, wa, wd, DE, c1=None):
     C = max(p.degree(DE.t), q.degree(DE.t))
 
     if q.degree(DE.t) > B:
-        eqs = [p.nth(i) - c1*q.nth(i) for i in range(B + 1, C + 1)]
+        eqs = [p.coeff_monomial((i,)) - c1*q.coeff_monomial((i,)) for i in range(B + 1, C + 1)]
         s = solve(eqs, c1)
         if not s or not s[0][c1].is_Rational:
             # deg(q) > B, no solution for c.
@@ -510,7 +510,7 @@ def parametric_log_deriv_heu(fa, fd, wa, wd, DE, c1=None):
     u1, r1 = (fa*l.quo(fd)).div(z)  # (l*f).div(z)
     u2, r2 = (wa*l.quo(wd)).div(z)  # (l*w).div(z)
 
-    eqs = [r1.nth(i) - c1*r2.nth(i) for i in range(z.degree(DE.t))]
+    eqs = [r1.coeff_monomial((i,)) - c1*r2.coeff_monomial((i,)) for i in range(z.degree(DE.t))]
     s = solve(eqs, c1)
     if not s or not s[0][c1].is_Rational:
         # deg(q) <= B, no solution for c.

diofant/integrals/risch.py

@@ -763,8 +763,8 @@ def as_poly_1t(p, t, z):
         one_t_part *= Poly(t**r, t)
 
     one_t_part = one_t_part.replace(t, z)  # z will be 1/t
-    if pd.nth(d):
-        one_t_part *= Poly(1/pd.nth(d), z, expand=False)
+    if pd.coeff_monomial((d,)):
+        one_t_part *= Poly(1/pd.coeff_monomial((d,)), z, expand=False)
     ans = t_part.as_poly(t, z, expand=False) + one_t_part.as_poly(t, z,
                                                                   expand=False)
 
@@ -1361,11 +1361,11 @@ def integrate_hyperexponential_polynomial(p, DE, z):
                 # If you get AttributeError: 'NoneType' object has no attribute 'nth'
                 # then this should really not have expand=False
                 # But it shouldn't happen because p is already a Poly in t and z
-                a = p.as_poly(z, expand=False).nth(-i)
+                a = p.as_poly(z, expand=False).coeff_monomial((-i,))
             else:
                 # If you get AttributeError: 'NoneType' object has no attribute 'nth'
                 # then this should really not have expand=False
-                a = p.as_poly(t1, expand=False).nth(i)
+                a = p.as_poly(t1, expand=False).coeff_monomial((i,))
 
             aa, ad = frac_in(a, DE.t, field=True)
             aa, ad = aa.cancel(ad, include=True)
@@ -1419,7 +1419,7 @@ def integrate_hyperexponential(a, d, DE, z=None, conds='piecewise'):
 
     qa, qd, b = integrate_hyperexponential_polynomial(pp, DE, z)
 
-    i = pp.nth(0, 0)
+    i = pp.coeff_monomial(1)
 
     ret = ((g1[0].as_expr()/g1[1].as_expr()).subs(s)
            + residue_reduce_to_basic(g2, DE, z))
@@ -1456,7 +1456,7 @@ def integrate_hypertangent_polynomial(p, DE):
     # XXX: Make sure that sqrt(-1) is not in k.
     q, r = polynomial_reduce(p, DE)
     a = DE.d.exquo(Poly(DE.t**2 + 1, DE.t))
-    c = Poly(r.nth(1)/(2*a.as_expr()), DE.t)
+    c = Poly(r.coeff_monomial((1,))/(2*a.as_expr()), DE.t)
     return q, c
 
 

diofant/logic/algorithms/dpll2.py

@@ -95,13 +95,13 @@ def __init__(self, clauses, variables, var_settings, symbols=None,
             self.heur_lit_unset = self._vsids_lit_unset
             self.heur_clause_added = self._vsids_clause_added
 
-        else:  # pragma: no cover
+        else:
             raise NotImplementedError
 
         if 'none' == clause_learning:
             self.add_learned_clause = lambda x: None
             self.compute_conflict = lambda: None
-        else:  # pragma: no cover
+        else:
             raise NotImplementedError
 
         # Create the base level

diofant/logic/boolalg.py

@@ -343,7 +343,7 @@ def as_set(self):
         from ..sets import Intersection
         if len(self.free_symbols) == 1:
             return Intersection(*[arg.as_set() for arg in self.args])
-        else:  # pragma: no cover
+        else:
             raise NotImplementedError("Sorry, And.as_set has not yet been"
                                       " implemented for multivariate"
                                       " expressions")
@@ -409,7 +409,7 @@ def as_set(self):
         from ..sets import Union
         if len(self.free_symbols) == 1:
             return Union(*[arg.as_set() for arg in self.args])
-        else:  # pragma: no cover
+        else:
             raise NotImplementedError("Sorry, Or.as_set has not yet been"
                                       " implemented for multivariate"
                                       " expressions")
@@ -493,7 +493,7 @@ def as_set(self):
         """
         if len(self.free_symbols) == 1:
             return self.args[0].as_set().complement(S.Reals)
-        else:  # pragma: no cover
+        else:
             raise NotImplementedError("Sorry, Not.as_set has not yet been"
                                       " implemented for mutivariate"
                                       " expressions")

diofant/logic/inference.py

@@ -77,7 +77,7 @@ def satisfiable(expr, algorithm="dpll2", all_models=False):
     elif algorithm == "dpll2":
         from .algorithms.dpll2 import dpll_satisfiable
         return dpll_satisfiable(expr, all_models)
-    else:  # pragma: no cover
+    else:
         raise NotImplementedError
 
 

diofant/matrices/dense.py

@@ -795,7 +795,7 @@ def __delitem__(self, key):
                 del self._mat[j + i*self.cols]
             self.cols -= 1
             return
-        else:  # pragma: no cover
+        else:
             raise NotImplementedError
 
     # Utility functions