Return complexes such that no bounding rectangles of non-conjugate classmethod _refine_complexes ( complexes ) # Make real isolating intervals disjoint and sort roots. Map initial real root index to an index in a factor where classmethod _reals_index ( reals, index ) # Get real roots of a composite polynomial. Take heroic measures to make poly compatible with CRootOf. Return the root if it is trivial or a CRootOf object. classmethod _postprocess_root ( root, radicals ) # classmethod _new ( poly, index ) #Ĭonstruct new CRootOf object from raw data. Get a root of a composite polynomial by index. classmethod _indexed_root ( poly, index, lazy = False ) # Return postprocessed roots of specified kind. classmethod _get_roots ( method, poly, radicals ) # Get real root isolating intervals for a square-free factor. classmethod _get_reals_sqf ( currentfactor, use_cache = True ) # classmethod _get_reals ( factors, use_cache = True ) #Ĭompute real root isolating intervals for a list of factors. Internal function for retrieving isolation interval from cache. Get complex root isolating intervals for a square-free factor. classmethod _get_complexes_sqf ( currentfactor, use_cache = True ) # classmethod _get_complexes ( factors, use_cache = True ) #Ĭompute complex root isolating intervals for a list of factors. _eval_evalf ( prec, ** kwargs ) #Įvaluate this complex root to the given precision. _ensure_reals_init ( ) #Įnsure that our poly has entries in the reals cache. _ensure_complexes_init ( ) #Įnsure that our poly has entries in the complexes cache. classmethod _count_roots ( roots ) #Ĭount the number of real or complex roots with multiplicities. Make complex isolating intervals disjoint and sort roots. classmethod _complexes_sorted ( complexes ) # Map initial complex root index to an index in a factor where classmethod _complexes_index ( complexes, index ) # Get real and complex roots of a composite polynomial. Variables is huge and is given by the following formula if \(M = 0\):Įval_approx, eval_rational classmethod _all_roots ( poly, use_cache = True ) # The total number of monomials in commutative Generate a set of monomials of degree less than or equal to \(N\) and greater Given a set of variables \(V\) and a min_degree \(N\) and a max_degree \(M\) max_degrees And min_degrees Are Both Integers Min_degrees <= degree_list(monom) <= max_degrees,Ĭase I. Min_degree <= total_degree(monom) <= max_degree, Unless otherwise specified, min_degrees is either 0 orĪ generator of all monomials monom is returned, such that Max_degrees and min_degrees are either both integers or both lists. itermonomials ( variables, max_degrees, min_degrees = None ) # as_expr ( * gens ) #Ĭonvert a monomial instance to a SymPy expression. Monomial ( monom, gens = None ) #Ĭlass representing a monomial, i.e. Domain, Expr Monomials encoded as tuples # class.
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