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rent:7,bright:29,broadli:13,bromwich:5,bug:[0,31,32],build:31,built:[0,7,32],builtin:[10,25,29],bullet:26,bump:4,c1:[17,20],c2:[17,20],c:[1,2,9,10,13,14,17,24,25,28,30,32],c_0:[1,8,26],c_1:[8,11,17,20,26],c_2:[8,11,17,20,26],c_:17,c_k:[1,26],c_l:11,c_n:[8,20,26],ca:[4,11,14,17,24,26,30],cabral:30,cabralrosetti:[17,30],cach:[4,6,10,11,25],calc_laplace_paramet:5,calc_nod:4,calc_time_domain_solut:5,calcbn:19,calcul:[0,2,4,5,7,8,9,10,11,15,19,20,21,25,26,28,32],calculu:[4,5,7,27],call:[0,1,2,4,5,7,9,10,12,13,14,15,17,19,21,22,24,25,26,28,31,32],callabl:7,cambridg:[15,30],can:[0,1,2,4,5,6,7,8,9,10,11,12,13,14,15,17,19,20,21,24,25,26,27,28,29,30,31,32],cancel:[1,4,5,7,9,10,14,17,21,24,25,32],cannot:[8,10,14,17,23,24,31,32],canon:13,care:[0,1,7,9,14,20,32],carl:24,carlson:[18,30],carri:0,casi:24,catalan:[15,18,24,26],catastroph:[5,21,25],categori:[17,32],cauchi:[13,14],caus:[4,8,28],caution:[9,10],cbm:[11,14,17,30],cbrt:[13,29],cd:13,cdot:[2,4,9,11,15,19,22],cecm:[24,26,30],ceil:[15,29],center:[4,21],central:2,certain:[5,17,24,26],certainli:7,ch:1,chanc:32,chang:[4,7,9,10,24,25,28,31,32],chapter:[0,11,13,17],charact:[13,24],character:5,characterist:5,cheap:[4,28],chebyfit:[3,8],chebyshev:[3,18],check:[6,10,14,15,19,24,25,26,32],chi:[11,24],choic:[1,4,6,9,17,21],choleski:28,cholesky_decomposit:28,choos:[2,4,5,7,9,14,15,20,22],chop:[1,2,4,8,9,11,13,14,15,16,17,19,20,21,23,24,28],chosen:[2,5,9,11,13,15,17,21,24,25],chug:32,ci:4,circl:[4,17,21,24,25],circumst:21,circumv:4,cite:30,cl2:24,cl:24,claim:32,classic:24,clausen:[18,19],clausentheorem:19,cleanup:8,clear:[4,17],clearli:10,clone:0,close:[1,5,7,9,10,11,13,14,15,17,19,20,21,24,25,26,28,32],closer:5,closest:[7,21],cm:[20,30],cmath:[10,18,23],cn:[13,20],co:[0,1,2,4,6,9,10,11,13,14,15,16,17,19,20,21,24,28,29,32],code:[0,4,10,25,30,32],coeff:8,coeffici:[1,5,8,9,13,17,18,19,20,21,24,25,26],coffei:24,cohen:[5,9],coincid:[11,15,24],col:28,collect:25,color:29,column:[9,28],com:[4,9,11,14,15,17,19,24,30,31],combin:[7,8,9,11,13,17,26],combinator:15,combinatori:[18,27],come:32,comfort:28,comment:32,common:[4,11,12,13,18,27,32],commonli:[14,15,18],commun:5,comp:[11,30],compact:13,companion:25,compar:[9,13,14,15,19,22,25,28,32],comparison:[4,5,9,10,17,19,27],compat:[10,28],compil:[27,32],complain:32,complementari:[14,19,24],complet:[4,5,10,13,14,15,20,31],complex:[0,2,4,5,6,7,8,9,10,11,13,14,15,16,17,18,19,20,21,22,23,24,26,27,28,30,32],complex_numb:31,complexnumb:31,complic:9,compon:[27,29],composit:3,comprehens:[17,30],compris:13,comput:[1,2,4,5,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,28,30,32],computation:[15,19,20],compute_uv:28,concept:32,concern:[26,28],conclus:10,condit:[1,6,8,9,11,13],condition:9,confirm:24,confluent:[17,18],confus:[14,15,17,24],confusingli:17,conj:[11,20],conjug:[8,11,24,25,28],conjunct:9,connect:11,consecut:[4,9,15,24],conserv:4,consid:[4,7,13,15,17,20,25,26],consist:17,constant:[4,5,9,11,13,15,18,20,27,32],constitut:17,constraint:26,construct:[0,24],contain:[1,4,5,7,9,10,17,25,26,28,29,32],context:[0,5,15,25,27,32],continu:[2,5,6,9,11,13,15,17,19,24,32],contour:[2,5,17],contra:7,contrari:32,contrast:9,contribut:5,contriv:32,control:[0,6,9,10,17,25,32],conveni:[0,6,9,13,17,19,21,24,25,28],convent:[11,13,17,20,21,23,25,32],converg:[1,4,6,7,8,9,13,14,17,19,21,24,25],convers:[10,18,27,31,32],convert:[5,10,12,13,21,23,26,28,32],convex:16,coordin:[11,20,25],cope:4,copi:[25,28,30],copiou:9,corless:[21,30],correct:[4,9,10,14,17,21,26,27,30],correctli:[1,26,32],correl:32,correspond:[1,5,9,10,11,17,20,24,28,32],cosec:[16,23],cosh:[1,4,9,13,14,19,32],cosin:[1,4,6,11,14,16,17,23,24,28],cosm:28,cospi:[11,21],cost:[1,9,25],cot:[5,18,24,29],cotang:[16,23,26],could:[1,5,7,20,26],coulomb:18,count:[11,18,25,28],counterclockwis:[4,21],counterpart:9,cours:[4,6,14,15,28,30,32],cover:32,cplot:[11,13,21,29],crandal:24,crc:5,crd:[4,30],creat:[0,5,10,17,27],credit:3,criterion:7,critic:24,cross:[13,32],cs:[1,4],csc:[18,24],csch:9,ct:13,ctx:[4,5,7,10],ctx_mp:10,ctx_mp_python:10,cu:13,cube:21,cubic:7,cuboid:4,cumul:[14,15],current:[0,7,8,9,10,12,17,24,25,28,32],curv:27,custom:[0,4,24,25,26,29],cut:[5,13,14,15,17,19,21,23],cyclic:21,cyclotom:18,cylind:18,cylindr:11,cython:10,d0:11,d1:11,d2:11,d2f:7,d3:11,d4:11,d:[2,5,9,10,11,13,17,19,20,24,25,30],d_n:11,dal:4,dash:29,data:[4,10,24],date:31,davi:5,david:[26,32],de:[17,24],deal:4,dealt:4,debug:27,decai:[4,5,9,11],decemb:30,decim:[0,1,5,9,10,25,26,27],decor:[0,25],decreas:[4,5,6,9,11,17,23],dedekind:[13,22],def:[0,1,2,7,13,17,20,21],defin:[1,2,4,6,9,11,13,14,15,17,19,20,21,22,23,24,25,26,28,29,32],defind:9,definit:[9,10,13,14,15,17,19,20,21,23,24,25,28,30,32],deform:5,deg:12,degener:[13,24],degre:[1,4,5,6,17,18,20,26],dehoog:5,delet:[4,31],delta:[10,19],demo:31,demonstr:[17,26],denomin:[15,26],denot:[0,4,13,14,17,19,20,21,22,24,28],densiti:14,depend:[1,4,5,7,10,14,17,24,25,26,28,31,32],deq:20,deriv:[3,4,6,7,8,9,11,13,15,17,19,21,24,32],describ:[0,4,5,6,9,11],descript:[0,4,5,10,25],descriptor:4,design:[4,10,32],desir: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usage","Function approximation","Differentiation","Numerical calculus","Numerical integration (quadrature)","Numerical inverse Laplace transform","Ordinary differential equations","Root-finding and optimization","Polynomials","Sums, products, limits and extrapolation","Contexts","Bessel functions and related functions","Mathematical constants","Elliptic functions","Exponential integrals and error functions","Factorials and gamma functions","Hyperbolic functions","Hypergeometric functions","Mathematical functions","Number-theoretical, combinatorial and integer functions","Orthogonal polynomials","Powers and logarithms","q-functions","Trigonometric functions","Zeta functions, L-series and polylogarithms","Utility functions","Number identification","Welcome to mpmath\u2019s documentation!","Matrices","Plotting","References","Setting up mpmath","Precision and representation 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