a d8d9Z?d:d;Z@dd?ZBdS)CzIFunctions for generating interesting polynomials, e.g. for benchmarking. )AddMulSymbolsympifyDummysymbols)Tuple)S)sqrt) nextprime) dmp_add_termdmp_negdmp_muldmp_sqr)dmp_zerodmp_one dmp_grounddup_from_raw_dict dmp_raise dup_random)ZZ)dup_zz_cyclotomic_poly)DMP)PolyPurePoly) _analyze_gens)subsetspublic filldedentNFcCsddlm}|dkr td||dur2t|ntd}|dkrd}tdg}td|dD]}t|}|t|q^|t |||d S|dkr|dd}nZ|dkr|d d |dd}n8|dkr|d d |dd|d d|dd}|r t ||S|S)aGenerates n-th Swinnerton-Dyer polynomial in `x`. Parameters ---------- n : int `n` decides the order of polynomial x : optional polys : bool, optional ``polys=True`` returns an expression, otherwise (default) returns an expression. )minimal_polynomialrz6Cannot generate Swinnerton-Dyer polynomial of order %sNx)polys (i`ii@) Z numberfieldsr ValueErrorrrr ranger appendrr)nr!r$r paiexr2h/Users/vegardjervell/Documents/master/model/venv/lib/python3.9/site-packages/sympy/polys/specialpolys.pyswinnerton_dyer_polys,   0r4cCs^|dkrtd|ttt|tt}|dur>t||}nt|td}|rV|S| S)aGenerates cyclotomic polynomial of order `n` in `x`. Parameters ---------- n : int `n` decides the order of polynomial x : optional polys : bool, optional ``polys=True`` returns an expression, otherwise (default) returns an expression. rz1Cannot generate cyclotomic polynomial of order %sNr!) r*rrintrrnewrras_expr)r-r!r$polyr2r2r3cyclotomic_polyAs r9cOs~t|}|dks |t|ks |s2td||fn(|s>tj}ntddt|t|D}|ddsj|St |g|RSdS)zGenerates symmetric polynomial of order `n`. Returns a Poly object when ``polys=True``, otherwise (default) returns an expression. rz7Cannot generate symmetric polynomial of order %s for %scSsg|] }t|qSr2)r).0sr2r2r3 kz"symmetric_poly..r$FN) rlenr*r ZOnerrr5getr)r-Zgensargsr8r2r2r3symmetric_poly\s rAcCs(tt||||||d}|r |S|S)a\Generates a polynomial of degree ``n`` with coefficients in ``[inf, sup]``. Parameters ---------- x `x` is the independent term of polynomial n : int `n` decides the order of polynomial inf Lower limit of range in which coefficients lie sup Upper limit of range in which coefficients lie domain : optional Decides what ring the coefficients are supposed to belong. Default is set to Integers. polys : bool, optional ``polys=True`` returns an expression, otherwise (default) returns an expression. )domain)rrr7)r!r-infsuprBr$r8r2r2r3 random_polyssrEr!yc stdd}ttr(td|fn|r>|tj@r>d}t|trZtd||f}n|rp|t|j@rpd}|sttdg}tfddt |D}t |D]>|}tfddt |D}| ||qt d dt ||DS) zConstruct Lagrange interpolating polynomial for ``n`` data points. If a sequence of values are given for ``X`` and ``Y`` then the first ``n`` values will be used. free_symbolsNz%s:%sFz~ Expecting symbol for x that does not appear in X or Y. 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