K ifdZddlmZmZmZmZmZddlmZddl m Z m Z m Z m Z mZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZm Z m!Z!m"Z"m#Z#m$Z$m%Z%m&Z&m'Z'm(Z(m)Z)m*Z*m+Z+m,Z,m-Z-m.Z.ddl/m0Z0ddl1m2Z2m3Z3m4Z4m5Z5ddl6m7Z7ddl8m9Z9m:Z:m;Z;mZ>m?Z?dd l@mAZAdd lBmCZCdd lDmEZEdd lFmGZGdd lHmIZIddlJmKZKe7Dcgc]}|jc}\ZMZNZOZPZQZRZSdZTdZUdZVdZWdZXdZYdZZdZ[dZ\dZ]dZ^dZ_dZ`dZadZbdZcdZdd Zed!Zfd"Zgd#Zhd$Zid%Zjd&Zkd'Zld(Zmd)Znd*Zod+Zpd,Zqd-Zrd.Zsd/Ztd0Zud1Zvd2Zwd3Zxy4cc}w)5z.Tests for dense recursive polynomials' tools. ) dup_normal dmp_normaldup_from_raw_dict dmp_convertdmp_swap)dmp_mul_ground)%dup_clear_denomsdmp_clear_denoms dup_integrate dmp_integratedmp_integrate_indup_diffdmp_diff dmp_diff_indup_evaldmp_eval dmp_eval_in dmp_eval_taildmp_diff_eval_in dup_trunc dmp_truncdmp_ground_trunc dup_monicdmp_ground_monic dup_contentdmp_ground_content dup_primitivedmp_ground_primitive dup_extractdmp_ground_extract dup_real_imag dup_mirror dup_scale dup_shift dmp_shift dup_transform dup_compose dmp_compose dup_decomposedmp_liftdup_sign_variations dup_revert dmp_revert)ANP)MultivariatePolynomialErrorExactQuotientFailed NotReversible DomainError)f_polys)FFZZQQZZ_IQQ_IEXRR)ring)I)S)sin)x)raisesc tgdtgk(sJtgdtgk(sJttdgdttdtdgk(sJttdgdttddtdtdgk(sJttdtdtdgdttdtdtdgk(sJttdtdtdgdttddtdtdtdgk(sJttdtdtdgdttddtddtddtdtdgk(sJttdtdtdgdttddtddtddtdtdtdgk(sJttdtditdttd tdd itk(sJtttdtddd tdtttdd tdd d tk(sJy)Nr < i@t)rGi)rI)r r6rg/mnt/ssd/data/python-lab/Trading/venv/lib/python3.12/site-packages/sympy/polys/tests/test_densetools.pytest_dup_integraterO6sa Q #r )) ) Q #r )) ) "Q%!R (RUBqEN :: : "Q%!R (R1Xr!ube,D DD D "Q%A1.2 6 A1r!u   "Q%A1.2 6 Aq2a5"Q%A' (( ( "Q%A1.2 6 ArBq!HbAh1r!u5 66 6 "Q%A1.2 6 ArBq"Ir!QxA1r!u= >> > *B2<z'test_dmp_integrate_in..ps/1b!R@rMc*tdddtSNrBrDrVrWsrNrYz'test_dmp_integrate_in..qs/1aB?rM) rf_6r5r6r rr r@ IndexErrorrWs@rNtest_dmp_integrate_inr_`siCB#A Aq!Q + (1aAr2Aq" =q!Q L LL L Aq!Q + (1aAr2Aq" =q!Q L LL L Aq!Q + (1aAr2Aq" =q!Q L LL L Aq!Q + (1aAr2Aq" =q!Q L LL L :@A :?@rMc Vtgdtgk(sJtdgdtgk(sJtddgdtdgk(sJtgddtddgk(sJtgddtgdk(sJtgddtgdk(sJtgd t}t|d t|k(sJt|dtgd k(sJt|dttt|dtdtk(sJt|d tttt|dtdtdtk(sJtd }tgd |}t|d|tgd |k(sJt|d|tgd|k(sJt|d |tg|k(sJt|d ||k(sJt|d|tt|d|d|k(sJt|d |ttt|d|d|d|k(sJy)NrBrCrBrCrB)rBrCrDr\)rDr\rDrBrUrrrC)r\rr) rH"8iLrrrErDrar) i2iii|rrrDrD) rCrrBrrrCrrrr)rBrrrCrrr)rr5rr4)rXKs rN test_dup_diffrmts0 B2 " $$ $ QCB 2 %% % QFAr "qc )) ) Iq" %!Q // / L!R (I 55 5 $a , == ==rBA Aq"  "" " Aq" !N NN N Aq" (1a*1E FF FrMc tgddtgk(sJtggddtggk(sJtgggddtgggk(sJtdgdgggddtgggk(sJtdgggggddtdgggk(sJtdggdgggggddtdggdgggk(sJtgdddttgddtk(sJttddttk(sJttddtdggggggdgggd gggggd ggd ggggd ggd dgggggggk(sJttddttttddtddtk(sJttddtttttddtddtddtk(sJt d}t td|}t|dd||k(sJt|dd|t|dd|k(sJt|dd|tt|dd|dd|k(sJt|dd|ttt|dd|dd|dd|k(sJy)NrBrrCrDrci !)rr)iyrriYi^rg)rr5rr]r4r)rlF_6s rN test_dmp_diffrts B1b !R '' ' RD!Q #t ++ + bTFAq" %2$ // / qcA3ZL!Q +v 55 5 qcURDM1a ,1# 77 7 qcUaSEB4(!Q 3!u~ EE E $aB /!1b) ** * CAr "c )) ) CAr "$2$'7$b"l;<vC5'B43%b!Wb1IB4P'R RR R  Q2 "8CAr#:Aq"E FF F CAr "h#q!R(!Q3Q2'? ?? ? 2A S!Q C CAq !S (( ( CAq !Xc1a%; ;; ; CAq !XhsAq!.DaA%N NN N CAq !X#q!Q'Aq11a&< << .s{32q"=rMc0ttdddtSr[rwrLrMrNrYz"test_dmp_diff_in..s{31a<rM)rr]r5rrr@r^rLrMrNtest_dmp_diff_inrysB sAq!R ((31a4aB?Aq"M NN N sAq!R ((31a4aB?Aq"M NN N sAq!R ((31a4aB?Aq"M NN N sAq!R ((31a4aB?Aq"M NN N :=> :<=rMctgdtdk(sJtddgdtdk(sJtgddtdk(sJy)NrarrBrCrBrCrDB)rr5rLrMrN test_dup_evalr}sK B2 ! ## # QFAr "a '' ' Iq" % ++ +rMctgddtdk(sJtggddtgk(sJtgggddtggk(sJtddggddtddgk(sJtdgggddtdggk(sJtddgggddtddggk(sJtddgddggddtddgk(sJtddggddgggddtddggk(sJy)NrDrrBrC rK)rr5rLrMrN test_dmp_evalrs B1b !Q && & RD!Q #r )) ) bTFAq" %" -- - aVHaB 'Aq6 11 1 qcUGQ2 &A3% // / q!fXJ1b )q!fX 55 5 aVaV$aB /B7 :: : q!fXAx(!Q 3Qy @@ @rMc fttdddttt tdddtddtk(sJttdddttt tdddtddtk(sJttdddtt tt tdddtddtdddtk(sJttdddtt tt tdddtddtdddtk(sJt dggggggt dgd ggt dt dt d t dggg}t|dddtdggggd gk(sJt td t td y)NrBrDrrarC-rUr)rrUricBtttdddtSrTrr]r5rLrMrNrYz"test_dmp_eval_in..s{31r1bArMcBtttdddtSr[rrLrMrNrYz"test_dmp_eval_in..s{31q!R@rM)rr]r5rrintr@r^rWs rNtest_dmp_eval_inrs  RAr &xQ1b'A2q"M NN N  Q1b %hsAq!R&@!QK LL L sB1b )X#q!Q+RB7Aq".F FF F sAq!R (H#q!Q+Q261a-E EE E r7)rdRDCG9rdBQQRRUVWRX8Y"Z[A q"aB ' r2'( )) ) :AB :@ArMctggdgdtgk(sJtgggdgdtggk(sJtgggddgdtgk(sJttgdttk(sJttgddtdk(sJttddgdtgdk(sJttdgdtddgd ggd gk(sJttddgdtgd k(sJttd d gdtgd k(sJtt d d gdtgdk(sJtt ddgdtgdk(sJttddgdtgdk(sJttgdd tgdk(sJy)NrBrC)rBrKiJrrK)irDiOSrD)i.QrB)ixiS=i#ii)iriBi8ri)Rii8iirU) lo ilfc5 ly ? i(l2c[l|U78lXLk^i)rUiiiX)rrCr\)irri) rr5f_0f_1f_2f_3f_4f_5r]rLrMrNtest_dmp_eval_tailrs "sAr *b 00 0 2$!a , 44 4 2$!QB /2 55 5 b!R (C // / k1b 1U :: : sAh2 .2C CC C qc1b )r1gsL-I II I sAh2 .2M MM M  c1Xq" !A BB B  c1Xq" !G HH H  b"Xq" "\ \\ \ r2h2 .2J JJ J iB /3E EE ErMc Lttddddttt t tdddtddtddtk(sJttddddttt tddtddtk(sJt tdy)NrCrarBrDrcDttdtdddtSr[)rr]r5rLrMrNrYz'test_dmp_diff_eval_in..s/Q1q!RHrM)rr]r5rrrr@r^rLrMrNtest_dmp_diff_eval_inrs CAq!R 0(31a4aB?ArJ KK K CAq!R 0#q!R(!Q3 44 4 :HIrMc tdd tdtddtdtdd tdtdg}tddtdtddtdtddtdtdg}t|dt|k(sJttd y) NrBrrkrC=rJrKcLttdtdgdtS)NrBrrD)r,r6rLrMrNrYz!test_dup_revert..s*beRU^Q"CrM)r6r,r@r1rXgs rNtest_dup_revertr s Q*beR2Y11ay"Q%AGA BbeR2Y1r!QxA1FA aB 1 $$ $ =CDrMc tdd tdtddtdtdd tdtdg}tddtdtddtdtddtdtdg}t|ddt|k(sJttd y) NrBrrrkrCrrJrKc*tdggddtSNrBrC)r-r6rLrMrNrYz!test_dmp_revert..s QC5!Q0KrM)r6r-r@r/rs rNtest_dmp_revertrs Q*beR2Y11ay"Q%AGA BbeR2Y1r!QxA1FA aAr "a '' ' &(KLrMctgdtdtgdk(sJtgdtdtgdk(sJt}t|d|d|dg|d||d|d gk(sJtd}t|d|d|dg|d||d|d gk(sJy) NrBrCrDr\rJrorD)rBrUrrBrUr)rorJr\rDrCrB)rUrBrrUrBr\rJrBrUr)rr5r7r4)Rrls rNtest_dup_truncrs 'A 37K KK K 'A 37H HH H A adAaD!A$'1q 1adAbE] BB B 1A adAaD!A$'1q 1adAaD\ AA ArMctggddgdtggk(sJtddggddggddgdtdgdggk(sJy)NrBrC)rBr\rBrd)rr5rLrMrNtest_dmp_truncr(sU bTAq61b )bT 11 1 q!fi!-1vq" =2$ LL LrMctttddttgddgggggdgddgggdtk(sJy)NrDrC)rBrUrrU)rBrUrBrB)rrr5rrLrMrNtest_dmp_ground_truncr-sO CA2 .2$ " J'D Eq" N NN NrMcxtgdtgdk(sJttdtgtgk(sJtt dgtt dgk(sJtt dt dt dgtt dt ddt dgk(sJy)NrDro r{c&tgdtS)N)rDr\rJ)rr5rLrMrNrYz test_dup_monic..6s )R(@rMrBrarD)rr5r@r0r6rLrMrNtest_dup_monicr3s Y #y 00 0  @A R  "" " beWb !beW ,, , beRUBrF+R 0RUBq!Hbe4L LL LrMctgddtgdk(sJtdgdgdggdtdgdgdggk(sJttd tggdtggk(sJtt dggdtt dggk(sJtt d gt dgt d ggdtt dgt dd gt dggk(sJy) Nrrr{rDrorrBrCc0tdgdgdggdtS)NrDr\rJrB)rr5rLrMrNrYz'test_dmp_ground_monic..Cs%5sQC!oq"%MrMrar)rr5r@r0r6rLrMrNtest_dmp_ground_monicr=s Iq" - :: : aS1#sOQ 3aS1# FF F MO RD!R (RD 00 0 beWIq" -2a5' :: :  Q%2a5'BrF8$a -24Q%2a8*r!ug0N OO OrMctgttdk(sJtdgttdk(sJtdgttdk(sJtddgttdk(sJtddgttdk(sJtgdttdk(sJtgdttdk(sJttddtdd gttdd k(sJttddtdd gttdd k(sJy) NrrBrUrCrb)rCr\rCrDr\rrJ)rr5r6rLrMrNtest_dup_contentrKs r2 "Q% '' ' sB 2a5 (( ( tR BqE )) ) 1vr "be ++ + 1vr "be ++ + y" %A .. . y" %A .. . 1a"Q(+R 0Bq!H << < 1a"Q(+R 0Bq"I == =rMc:tggdttdk(sJtggdttdk(sJtdggdttdk(sJtdggdttdk(sJtdgdggdttdk(sJtdgdggdttdk(sJtdgdgdggdttdk(sJtdgdgdggdttdk(sJttddgtddggdttddk(sJttddgtddggdttdd k(sJttdttdk(sJtt ttddtdttdk(sJtt dttdk(sJtt t tddtdttdk(sJtt dttdk(sJtt t tddtdttdk(sJttdttdk(sJtt ttddtdttdk(sJttdttdk(sJtt ttd dtdttd k(sJttdttdk(sJtt ttd dtdttd k(sJttdttdk(sJtt ttd dtdttd k(sJy) NrBrrUrCr\rDrrJrrorarK) rr5r6rrrrrrrr]rLrMrNtest_dmp_ground_contentrXs rdAr *be 33 3 rdAr *be 33 3 seQ +r!u 44 4 tfa ,1 55 5 sQCj!R 0BqE 99 9 sQCj!R 0BqE 99 9 sQC!oq" 5A >> > sQC!oq" 5A >> > 1azBq!H:62 >"Q( JJ J 1azBq!H:62 >"Q) KK K c1b )RU 22 2 sBqE1b)1b 257U ;; ; c1b )RU 22 2 sBqE1b)1b 257U ;; ; c1b )RU 22 2 sBqE1b)1b 257U ;; ; c1b )RU 22 2 sBqE1b)1b 257U ;; ; c1b )RU 22 2 sBqE1b)1b 257U ;; ; c1b )RU 22 2 sBqE1b)1b 257U ;; ; c1b )RU 22 2 sBqE1b)1b 257U ;; ;rMctgttdgfk(sJttdgttdtdgfk(sJttdtdgttdtdtdgfk(sJttdtdgttdtdtdgfk(sJttdtdtdgttdtdtdtdgfk(sJttdtdtdgttdtdtdtdgfk(sJtgttdgfk(sJttdgttdtdgfk(sJttdtdgttdtdtdgfk(sJttdtdgttdtdtdgfk(sJttdtdtdgttdtdtdtdgfk(sJttdtdtdgttdtdtdtdgfk(sJttddtddgttddtdtdgfk(sJttddtddgttddtdtd gfk(sJy) NrrBrCr\rDrrJrro)rr5r6rLrMrNtest_dup_primitiversD R RUBK // / "Q%" %"Q%"Q%)9 99 9 "Q%A ,AA10G GG G "Q%A ,AA10G GG G  A1r!ur #')!ur!ubeRU.C&D EE E  A1r!ur #')!ur!ubeRU.C&D EE E R RUBK // / "Q%" %"Q%"Q%)9 99 9 "Q%A ,AA10G GG G "Q%A ,AA10G GG G  A1r!ur #')!ur!ubeRU.C&D EE E  A1r!ur #')!ur!ubeRU.C&D EE E  Aq2a8b "&(AhA1%? @@ @  Aq2a8b "&(Bi"Q%A%@ AA ArMcttdgdttdtdgfk(sJtggdttdggfk(sJttdttdtfk(sJttttddtdttdtfk(sJttdttdtfk(sJttttddtdttdtfk(sJtt dttdt fk(sJttt tddtdttdt fk(sJtt dttdt fk(sJttt tddtdttdt fk(sJttdttdtfk(sJttttddtdttdtfk(sJttdttdtfk(sJttttddtdttdtfk(sJttdttdtfk(sJttttd dtdttd tfk(sJttdggdttdtdggfk(sJttdggdttdtdggfk(sJttddgtdd ggdttdd tdgtdggfk(sJttddgtddggdttdd tdgtdggfk(sJy) NrBrrCrDr\rJrorarKrr) rr5rrrrrrrr]r6rLrMrNtest_dmp_ground_primitivers AB /BqEBqE73C CC C a ,A == = Q +1s| ;; ; sBqE1b)1b 268eS\ BB B Q +1s| ;; ; sBqE1b)1b 268eS\ BB B Q +1s| ;; ; sBqE1b)1b 268eS\ BB B Q +1s| ;; ; sBqE1b)1b 268eS\ BB B Q +1s| ;; ; sBqE1b)1b 268eS\ BB B Q +1s| ;; ; sBqE1b)1b 268eS\ BB B Q +1s| ;; ; sBqE1b)1b 268eS\ BB B "Q% 1b 1ber!ugY5G GG G "Q% 1b 1ber!ugY5G GG G  Q(bAhZ !R )-/1XA"Q%7I,J KK K  Q(bAhZ !R )-/2Y"Q%2a5'8J,K LL LrMctgdt}tgdt}tgdt}tgdt}t||td||fk(sJy)N),r!rbr)V r+r`r)@r0rrErrB)rrrkrr)rr5rrXrFGs rNtest_dup_extractrsS=rBA8"=A+R0A*B/A q!R UAqM 11 1rMc tdggdggdggdggdt}tdggdggdgggdt}td ggd ggd ggdggdt}td ggd ggdgggdt}t||dtd||fk(sJy)NrrrrrBrrrrrrErrrk)rr5r rs rNtest_dmp_ground_extractrs B 2xeW=q" FAXJWIrG9bA1bIARD"rdBb1#62>ASE2ub2$3Q;A aAr *uam ;; ;rMc tgtggggfk(sJtdgtdggggfk(sJtddgtdgdggddggfk(sJtddgtdgdggddggfk(sJtgdtdgdggdgddgddggfk(sJttdtdtdtdgttdggtdtdtdgtdggtdtdggtdtdtdtdggfk(sJttd y) NrBrrCr{)rUrrDrDrdrUcJttdtdgtSr)r!r9rLrMrNrYz$test_dup_real_imag..s r!ubenb ArM)r!r5r@r2rLrMrNtest_dup_real_imagrsw R bTB4L 00 0 !b !sebT] 22 2 !Q $1#sq!fX(> >> > !Q $1#sq!fX(> >> > 2 C!j1QFQF3CD EE E "Q%A1r!u5r : Q%"r"vr!ube,r!ug6 Q%AbfbeRUBqE:;?    ;ABrMctgtgk(sJtdgtdgk(sJtgdtgdk(sJtgdtgdk(sJy)NrBrBrCrDr\rJrBrrDrrJr)rUrCrdr\ro)r"r5rLrMrNtest_dup_mirrorrs] b"  ## # qc2 1# %% % or *.? ?? ? (" -1F FF FrMctgdtgk(sJtdgdtdgk(sJtgddtgdk(sJtgddtgdk(sJy)NrUrBrri)ia iRirJ)r#r5rLrMrNtest_dup_scalersd RR B && & aS"b !aS (( ( _b" -1B BB B _b" -1J JJ JrMctgdtgk(sJtdgdtdgk(sJtgddtgdk(sJtgddtgdk(sJy)NrBr)rBrorrra)rBiSii )r$r5rLrMrNtest_dup_shiftrsd RB 2 %% % aS!R QC '' ' _a ,0B BB B _a ,0H HH HrMcttdtdgtdgdttdtdgk(sJtggtdtdgdtggk(sJtdtdggg}tdtdgtdtdgg}t|tdtdgdt|k(sJy)NrBrCrrD)r%r5)xyx1y2s rNtest_dmp_shiftrs beRU^beWa 4A1 FF F bTBqE2a5>1b 1bT 99 9 a5"Q%." B UBqENRUBqEN +D R"Q%AB /4 77 7rMctggddgtgk(sJtgdgddgtgk(sJtgddgddgtgk(sJtgdgdddgtgdk(sJy)NrBrC)rorr\rdrH)rBrdr\rd) roiiiciiMi'Cii)r&r5rLrMrNtest_dup_transformrs R!Q , 22 2 aS1a&" - 33 3 aVaVR 0B 66 6 +Z!R" E? @@ @rMc0tggtgk(sJtgdgtgk(sJtgddgtgk(sJtdggtdgk(sJtgdgtgk(sJtgdgtdgk(sJtgddgtdgk(sJtgddgtdgk(sJtgdddgtgd k(sJtgdddgtgd k(sJtgdgdtgd k(sJy) NrBrC)rBrCrrbr\rarrUrBrr)rBr\r\rBr\rKrKr\)r'r5rLrMrNtest_dup_composers r2r "b (( ( rA3 #r )) ) rAq62 &" ,, , sB #s ** * y"b )R // / y"b )aS 00 0 y1#r *qc 11 1 y1#r *rd 22 2 y1b'2 .) ;; ; y1a&" - :: : y)R 0O CC CrMc"tgdgddtgdk(sJtggggggdtgggk(sJtgggdgggdtgggk(sJtgggdggdgggdtgggk(sJtdggggdtdgggk(sJtdgdgggggdtggk(sJtdgdgdggggdtdggk(sJtdgdgdggdggdtdggk(sJtdgdgdggdggdtdggk(sJtdgdgdggdgd ggdtdggggk(sJtdgdgdggdgdggdtdgdgdggk(sJtdgdgdggdgdgdggdtdgdgd gd gdggk(sJy) NrbrrrCrBr\rarrUrK)r(r5rLrMrNtest_dmp_composer*s& y)Q 3 FF F vvq" -2$ 77 7 v!w2 .B4& 88 8 v!u~q" 52$ ?? ? !wAr *ug 55 5 aS#a 4 << < aS1#a 4! == = aS1#!q" 51# >> > aS1#!q" 52$ ?? ? aS1#!rd Q ;S# NN N aS1#!d Q ;aS1# NN N  qcA31#sQC!R 167S1#sQC!4M NN NrMcBtdgtdggk(sJtddgtddggk(sJtgdtgdgk(sJtgdtgdgdgk(sJtgdtgdgdgk(sJtgdtgdgdgk(sJtgd tgd gdgk(sJgd }t|tgd gd gk(sJgd}t|tgdgd gk(sJgd}t|tgdgd gk(sJtdt\}}d|dzzdz d|dzzdzd|dzzd|zzdzd|dzzd|zzdzd|dzzd |dzzzd!|zzd"zg}t||j|gk(sJy)#NrBr)rBrrr)rBrrrrr)rBrrrrrr)rarrrrB)rarrB)r\rrDrrC)r\rDrC) rBrrrririqrrir)rBrrrr)rBrrJr) rCr(ri,ririrri)rCrrrr) rBrrrii iiaiiXiVrG)rBrrkirGtrorC*r`rii ipi`rlrDi8ir)r)r5r; to_domain)rXrrs rNtest_dup_decomposer@s !b !qcU ** * !Q $!Q 00 0 r *|n << < " -)Y1G GG G r #'3Y&? @@ @ " -)Y1G GG G " -)Y1G GG G9A B $4l#C CC C.qs"Q%AB ?rM) r6r.mapr*algebraic_fieldr<r8r@r2)qf_af_liftf_gs rN test_dmp_liftrcs Aq2a8R1X&A 1az1b !3r1b>3r1b> bAh1a !1b )32q 2a8/Da+L NCVV2 3F CB..q1 2f << < 7DGT!Wd1aj$q"+ >C CD !V ++ + ;?@rMcPtgtdk(sJtddgtdk(sJtgdtdk(sJtgdtdk(sJtgdtdk(sJtgdtdk(sJtgdtdk(sJtgdtdk(sJtgd tdk(sJtgd tdk(sJtgd tdk(sJtgd td k(sJtgdtd k(sJtgdtdk(sJtgdtdk(sJtgdtdk(sJtgdtdk(sJtgdtdk(sJtgdtdk(sJtgdtd k(sJtgdtd k(sJtgdtdk(sJtgdtdk(sJtgdtdk(sJy)NrrB)rBrrC)rBrrDr)rBrr\rrJ)rUrrC)rUrrDr)rUrr\rrJ)rUrr)rBrr)rBr\r)rBrrJrC)rUr\r)rUr\rJ)rUrrJ)rBr\rJ)rUrrrr)rBrrrr)rBrr\rr)rBrrrrJ)rUrr\rr)rUrrrrJ)r+r5rLrMrNtest_dup_sign_variationsrts r2 &! ++ + 1vr *a // / y" - 22 2 |R 0A 55 5  3q 88 8 z2 .! 33 3 }b 1Q 66 6 / 4 99 9 |R 0A 55 5 |R 0A 55 5 {B /1 44 4 {B /1 44 4 {B /1 44 4 z2 .! 33 3 {B /1 44 4 z2 .! 33 3 12 6! ;; ; 12 6! ;; ; 0" 5 :: : 0" 5 :: : 0" 5 :: : / 4 99 9 0" 5 :: : / 4 99 9rMctgtttdgfk(sJttdgtttdtdgfk(sJttdgtttdtdgfk(sJttddgttdtdgfk(sJttddgtttdtdgfk(sJttdtdtdgtttdtdtdtdgfk(sJttdtddtdgtttdtdtdtdgfk(sJttdtdtdgttdtdtdtdtdgfk(sJttdtddtdgttdtdtdtdtdgfk(sJttt ddz tt dd z gttd td tdgfk(sJttdgttdtdgfk(sJttt t t z tdgttt tt t tdgfk(sJtjt }t|d d t zd zz |dg|}t|dk(sJy)NrBrarDrrCTconvertrr\rogE/Xn @gjq @gp= ף@gz0(x + 0.353356890459364, [1.05971731448763, 0.0])) r r6r5r9r=r>r?r: frac_fieldstr)rresults rNtest_dup_clear_denomsr sF BB 'BqE2; 66 6 RUGR ,AA0@ @@ @ RUGR ,AA0@ @@ @ R1XJ +11w/? ?? ? R1XJB /BqEBqE73C CC C  A1r!ur2 '+-a52a5"Q%A2G*H II I  A1a"Q% "b *.0ebeRUBqE5J-K LL L RUB % qED *.0ebeRUBqE5J-K LL L RUB 1%!u2t -13AA1r!u8M0N OO O  AaDFR!QZ " &*,Q%"Q%A)@ AA A RUGR (RURUG,< << < RAq\2a512 62a52c!f:rRSuBU:V VV V aA q&(T/!:;QsVDa HF v;L LL LrMctggdtttdggfk(sJttdggdtttdtdggfk(sJttdggdtttdtdggfk(sJttddggdttdtdggfk(sJttddggdtttdtdggfk(sJttdgtdgggdtttdtdgtdgggfk(sJttdgtddgggdtttdtdgtdgggfk(sJttdtdtdgdttdtdtdtdtdgfk(sJttdtddtdgdttdtdtdtdtdgfk(sJttdgtdgggdttdtdtdgtdgggfk(sJttdgtddgggdttdtdtdgtdgggfk(sJttt ddz gtt dd z ggdttd td gtdggfk(sJttdggdttdtdggfk(sJttt t t z tdggdttt tt t tdggfk(sJy) NrBrarDrCrTrrr\ro)r r6r5r9r=r>r?rLrMrNtest_dmp_clear_denomsr s RD!R ,A == = beWIq"b 1ber!ugY5G GG G beWIq"b 1ber!ugY5G GG G bAhZL!R 0RUbeWI4F FF F bAhZL!R 4A"Q% 8J JJ J  Q%2a5'22r +/1!u1wA6L.M NN N b   AhZR )-/UbeWr!ugr4J,K LL L RUB % qEr2t -13AA1r!u8M0N OO O RUBq!Hb /  B &*,Q%"Q%A11F)G HH H beWr ( ' RT +/1!u1wA6L.M NN N beWr!Qxj"5q"b$( *.0er!ug1w5K-L MM M  QqT!V*1Q46 |$a -13A"Q%2a5'8J0K LL L beWIq" -"Q%2a5'1C CC C bQlBqE23Q ;1CPQFUWXYUZH[G\?] ]] ]rMN)y__doc__sympy.polys.densebasicrrrrrsympy.polys.densearithrsympy.polys.densetoolsr r r r r rrrrrrrrrrrrrrrrrrr r!r"r#r$r%r&r'r(r)r*r+r,r-sympy.polys.polyclassesr.sympy.polys.polyerrorsr/r0r1r2sympy.polys.specialpolysr3sympy.polys.domainsr4r5r6r7r8r9r:sympy.polys.ringsr;sympy.core.numbersr<sympy.core.singletonr=(sympy.functions.elementary.trigonometricr> sympy.abcr?sympy.testing.pytestr@to_denserrrrrrr]rOrQr_rmrtryr}rrrrrrrrrrrrrrrrrrrrrrrrrrrrr r rWs0rNrs}4 2((->>>" "8', AB&F4JEMBM N M O >';TA2'LT2<C&GKI8@D$N, 2FA":<M:^w%Hs<E