typing(polys): Add a few type hints in polys

sympy/polys/compatibility.py

@@ -1,5 +1,14 @@
 """Compatibility interface between dense and sparse polys. """
 
+from __future__ import annotations
+
+from typing import TYPE_CHECKING
+
+if TYPE_CHECKING:
+    from sympy.core.expr import Expr
+    from sympy.polys.domains.domain import Domain
+    from sympy.polys.orderings import MonomialOrder
+    from sympy.polys.rings import PolyElement
 
 from sympy.polys.densearith import dup_add_term
 from sympy.polys.densearith import dmp_add_term
@@ -230,11 +239,12 @@
 
 @public
 class IPolys:
-    symbols = None
-    ngens = None
-    domain = None
-    order = None
-    gens = None
+
+    gens: tuple[PolyElement, ...]
+    symbols: tuple[Expr, ...]
+    ngens: int
+    domain: Domain
+    order: MonomialOrder
 
     def drop(self, gen):
         pass

sympy/polys/fields.py

@@ -13,15 +13,16 @@
 from sympy.core.symbol import Symbol
 from sympy.core.sympify import CantSympify, sympify
 from sympy.functions.elementary.exponential import ExpBase
+from sympy.polys.domains.domain import Domain
 from sympy.polys.domains.domainelement import DomainElement
 from sympy.polys.domains.fractionfield import FractionField
 from sympy.polys.domains.polynomialring import PolynomialRing
 from sympy.polys.constructor import construct_domain
-from sympy.polys.orderings import lex
+from sympy.polys.orderings import lex, MonomialOrder
 from sympy.polys.polyerrors import CoercionFailed
 from sympy.polys.polyoptions import build_options
 from sympy.polys.polyutils import _parallel_dict_from_expr
-from sympy.polys.rings import PolyElement
+from sympy.polys.rings import PolyRing, PolyElement
 from sympy.printing.defaults import DefaultPrinting
 from sympy.utilities import public
 from sympy.utilities.iterables import is_sequence
@@ -104,8 +105,14 @@ def sfield(exprs, *symbols, **options):
 class FracField(DefaultPrinting):
     """Multivariate distributed rational function field. """
 
+    ring: PolyRing
+    gens: tuple[FracElement, ...]
+    symbols: tuple[Expr, ...]
+    ngens: int
+    domain: Domain
+    order: MonomialOrder
+
     def __new__(cls, symbols, domain, order=lex):
-        from sympy.polys.rings import PolyRing
         ring = PolyRing(symbols, domain, order)
         symbols = ring.symbols
         ngens = ring.ngens
@@ -280,7 +287,6 @@ def to_domain(self):
         return FractionField(self)
 
     def to_ring(self):
-        from sympy.polys.rings import PolyRing
         return PolyRing(self.symbols, self.domain, self.order)
 
 class FracElement(DomainElement, DefaultPrinting, CantSympify):

sympy/polys/polyclasses.py

@@ -140,6 +140,9 @@ class DMP(CantSympify):
 
     __slots__ = ()
 
+    lev: int
+    dom: Domain
+
     def __new__(cls, rep, dom, lev=None):
 
         if lev is None:

sympy/polys/polyoptions.py

@@ -4,7 +4,9 @@
 
 __all__ = ["Options"]
 
-from sympy.core import Basic, sympify
+from sympy.core.basic import Basic
+from sympy.core.expr import Expr
+from sympy.core.sympify import sympify
 from sympy.polys.polyerrors import GeneratorsError, OptionError, FlagError
 from sympy.utilities import numbered_symbols, topological_sort, public
 from sympy.utilities.iterables import has_dups, is_sequence
@@ -123,6 +125,9 @@ class Options(dict):
     __order__ = None
     __options__: dict[str, type[Option]] = {}
 
+    gens: tuple[Expr, ...]
+    domain: sympy.polys.domains.Domain
+
     def __init__(self, gens, args, flags=None, strict=False):
         dict.__init__(self)
 

sympy/polys/polytools.py

@@ -1,5 +1,6 @@
 """User-friendly public interface to polynomial functions. """
 
+from __future__ import annotations
 
 from functools import wraps, reduce
 from operator import mul
@@ -164,7 +165,7 @@ class Poly(Basic):
     is_Poly = True
     _op_priority = 10.001
 
-    def __new__(cls, rep, *gens, **args):
+    def __new__(cls, rep, *gens, **args) -> Poly:
         """Create a new polynomial instance out of something useful. """
         opt = options.build_options(gens, args)
 

sympy/polys/rings.py

@@ -15,11 +15,12 @@
 from sympy.polys.compatibility import IPolys
 from sympy.polys.constructor import construct_domain
 from sympy.polys.densebasic import ninf, dmp_to_dict, dmp_from_dict
+from sympy.polys.domains.domain import Domain
 from sympy.polys.domains.domainelement import DomainElement
 from sympy.polys.domains.polynomialring import PolynomialRing
 from sympy.polys.heuristicgcd import heugcd
 from sympy.polys.monomials import MonomialOps
-from sympy.polys.orderings import lex
+from sympy.polys.orderings import lex, MonomialOrder
 from sympy.polys.polyerrors import (
     CoercionFailed, GeneratorsError,
     ExactQuotientFailed, MultivariatePolynomialError)
@@ -33,7 +34,7 @@
 from sympy.utilities.magic import pollute
 
 @public
-def ring(symbols, domain, order=lex):
+def ring(symbols, domain, order: MonomialOrder|str = lex):
     """Construct a polynomial ring returning ``(ring, x_1, ..., x_n)``.
 
     Parameters
@@ -196,6 +197,12 @@ def _parse_symbols(symbols):
 class PolyRing(DefaultPrinting, IPolys):
     """Multivariate distributed polynomial ring. """
 
+    gens: tuple[PolyElement, ...]
+    symbols: tuple[Expr, ...]
+    ngens: int
+    domain: Domain
+    order: MonomialOrder
+
     def __new__(cls, symbols, domain, order=lex):
         symbols = tuple(_parse_symbols(symbols))
         ngens = len(symbols)

sympy/polys/rootoftools.py

@@ -1,6 +1,7 @@
 """Implementation of RootOf class and related tools. """
 
 
+
 from sympy.core.basic import Basic
 from sympy.core import (S, Expr, Integer, Float, I, oo, Add, Lambda,
     symbols, sympify, Rational, Dummy)

sympy/polys/subresultants_qq_zz.py

@@ -336,7 +336,7 @@ def sylvester(f, g, x, method = 1):
         return M
 
     # Sylvester's matrix of 1853 (a.k.a sylvester2)
-    if method >= 2:
+    else:
         if len(fp) < len(gp):
             h = []
             for i in range(len(gp) - len(fp)):