ó ¡¼™\c@ sLddlmZmZddlmZddlmZd„Zd„ZdS(iÿÿÿÿ(tprint_functiontdivision(trange(twrapsc s|‰‡fd†}|S(s} Memo decorator for sequences defined by recurrence See usage examples e.g. in the specfun/combinatorial module c s"tˆƒ‡‡fd†ƒ}|S(Nc s`tˆƒ}||dkr$ˆ|Sx1t||dƒD]}ˆjˆ|ˆƒƒq8WˆdS(Niiÿÿÿÿ(tlenRtappend(tntLti(tcachetf(s:lib/python2.7/site-packages/sympy/utilities/memoization.pytgs  (R(R R (R (R s:lib/python2.7/site-packages/sympy/utilities/memoization.pyt decorators((tinitialR ((R s:lib/python2.7/site-packages/sympy/utilities/memoization.pytrecurrence_memos c sg‰‡‡fd†}|S(sé Memo decorator for associated sequences defined by recurrence starting from base base_seq(n) -- callable to get base sequence elements XXX works only for Pn0 = base_seq(0) cases XXX works only for m <= n cases c s%tˆƒ‡‡‡fd†ƒ}|S(Nc s­tˆƒ}||kr$ˆ||Sxzt||dƒD]e}ˆ|ƒ}|g}ˆj|ƒx:td|dƒD]%}ˆ||ˆƒ}|j|ƒqtWq8Wˆ||S(Ni(RRR(RtmRRtF_i0t F_i_cachetjtF_ij(tbase_seqR R (s:lib/python2.7/site-packages/sympy/utilities/memoization.pyR )s      (R(R R (RR (R s:lib/python2.7/site-packages/sympy/utilities/memoization.pyR (s!((RR ((RR s:lib/python2.7/site-packages/sympy/utilities/memoization.pytassoc_recurrence_memos N( t __future__RRtsympy.core.compatibilityRtsympy.core.decoratorsRRR(((s:lib/python2.7/site-packages/sympy/utilities/memoization.pyts