# `stdlib` - The standard library

## Table of contents

1. `glossary` - glossary
2. `mathematical constants and functions` - an overview
3. `:=` - assign variables
4. `.` - concatenate objects
5. `..` - range operator
6. `=, <>` - equations and inequalities
7. `<,<=,>,>=` - inequalities
8. `+` - add expressions
9. `-` - subtract expressions
10. `*` - multiply expressions
11. `/` - divide expressions
12. `^` - raise an expression to a power
13. `@` - compose functions
14. `@@` - iterate a function
15. `$` - create an expression sequence
16. `_exprseq` - expression sequences
17. `_index` - indexed access
18. `intersect, minus, union` - operators for sets and intervals
19. `_invert` - the reciprocal of an expression
20. `_lazy_and, _lazy_or` - ``lazy evaluation'' of Boolean expressions
21. `_negate` - the negative of an expression
22. `_stmtseq` - statement sequences
23. `%if` - conditional creation of code by the parser
24. `Ci` - the cosine integral function
25. `D` - differential operator for functions
26. `DIGITS` - the significant digits of floating point numbers
27. `Ei` - the exponential integral function
28. `FAIL` - indicate a failed computation
29. `Line-Editor` - editing lines in the terminal version of MuPAD
30. `NIL` - the singleton element of the domain `DOM_NIL`
31. `NOTEBOOKFILE, NOTEBOOKPATH` - Notebook file name and path
32. `O` - the domain of order terms (Landau symbols)
33. `ORDER` - the default number of terms in series expansions
34. `path variables` - file search paths
35. `PRETTYPRINT` - control the formatting of output
36. `Re, Im` - real and imaginary part of an arithmetical expression
37. `RootOf` - the set of roots of a polynomial
38. `Si` - the sine integral function
39. `TESTPATH` - write path for `prog::test`
40. `TEXTWIDTH` - the maximum number of characters in an output line
41. `TRUE, FALSE, UNKNOWN` - Boolean constants
42. `UNIX` - MuPAD command line options and initialization files for UNIX
43. `abs` - the absolute value of a real or complex number
44. `alias, unalias` - defines or un-defines an abbreviation or a macro
45. `anames` - identifiers that have values or properties
46. `and, or, not` - Boolean operators
47. `append` - add elements to a list
48. `arcsin,arccos,arctan,arccsc,arcsec,arccot` - the inverse trigonometric functions
49. `arcsinh, arccosh, arctanh, arccsch, arcsech, arccoth` - the inverse hyperbolic functions
50. `arg` - the argument (polar angle) of a complex number
51. `args` - access procedure parameters
52. `array` - create an array
53. `assign` - perform assignments given as equations
54. `assignElements` - assign values to entries of an array, a list, or a table
55. `assume` - attach a property to an identifier
56. `asympt` - compute an asymptotic series expansion
57. `bernoulli` - the Bernoulli numbers and polynomials
58. `besselI, besselJ, besselK, besselY` - the Bessel functions
59. `beta` - the beta function
60. `binomial` - binomial coefficients
61. `bool` - Boolean evaluation
62. `break` - terminate a loop or a `case` switch prematurely
63. `builtin` - representatives of C-functions of the MuPAD kernel
64. `bytes` - the memory used by the current MuPAD session
65. `case` - switch statement
66. `ceil,floor,round,trunc` - rounding to an integer
67. `coeff` - the coefficients of a polynomial
68. `coerce` - type conversion
69. `collect` - collect coefficients of a polynomial expression
70. `combine` - combine terms of the same algebraic structure
71. `complexInfinity` - complex infinity
72. `conjugate` - complex conjugation
73. `contains` - test if an entry exists in a container
74. `content` - the content of a polynomial
75. `context` - evaluate an object in the enclosing context
76. `debug` - execute a procedure in single-step mode
77. `degree` - the degree of a polynomial
78. `degreevec` - the exponents of the leading term of a polynomial
79. `delete` - delete the value of an identifier
80. `denom` - the denominator of a rational expression
81. `diff` - differentiate an expression or a polynomial
82. `dilog` - the dilogarithm function
83. `dirac` - the Dirac delta distribution
84. `discont` - discontinuities of a function
85. `div` - the integer part of a quotient
86. `divide` - divide polynomials
87. `domtype` - the data type of an object
88. `end` - close a block statement
89. `erf,erfc` - the error function and the complementary error function
90. `error` - raise a user-specified exception
91. `eval` - evaluate an object
92. `evalassign` - assignment with evaluation of the left hand side
93. `evalp` - evaluate a polynomial at a point
94. `exp` - the exponential function
95. `expand` - expand an expression
96. `export, unexport` - export library functions or undo the export
97. `expose` - display the source code of a procedure or the entries of a domain
98. `expr` - convert into an element of a basic domain
99. `expr2text` - convert objects into character strings
100. `external` - create a module function environment
101. `extnops` - the number of operands of a domain element
102. `extop` - the operands of a domain element
103. `extsubsop` - substitute operands of a domain element
104. `fact` - the factorial function
105. `factor` - factor a polynomial into irreducible polynomials
106. `fclose` - close a file
107. `finput` - read MuPAD objects from a file
108. `float` - convert to a floating point number
109. `fopen` - open a file
110. `for` - for loop
111. `fprint` - write data to a file
112. `frac` - the fractional part of a number
113. `fread` - read and execute a file
114. `freeze,unfreeze` - create an inactive or active copy of a function
115. `ftextinput` - read a text file
116. `funcenv` - create a function environment
117. `gamma` - the gamma function
118. `gcd` - the greatest common divisor of polynomials
119. `gcdex` - the extended Euclidean algorithm for polynomials
120. `genident` - create an unused identifier
121. `genpoly` - create a polynomial using the ``b''-adic expansion
122. `getpid` - the process ID of the running MuPAD kernel
123. `getprop` - query properties of expressions
124. `ground` - ground term (constant coefficient) of a polynomial
125. `has` - check if an object occurs in another object
126. `hastype` - test if an object of a specified type occurs in another object
127. `heaviside` - the Heaviside step function
128. `help` - display a help page
129. `history` - access an entry of the history table
130. `hold` - delay evaluation
131. `icontent` - the content of a polynomial with rational coefficients
132. `if` - branch statement
133. `id` - the identity map
134. `ifactor` - factor an integer into primes
135. `igamma` - the incomplete Gamma function
136. `igcd` - the greatest common divisor of integers
137. `igcdex` - the extended Euclidean algorithm for two integers
138. `ilcm` - the least common multiple of integers
139. `in` - membership
140. `indets` - the indeterminates of an expression
141. `indexval` - indexed access to arrays and tables without evaluation
142. `infinity` - infinity
143. `info` - prints short information
144. `input` - interactive input of MuPAD objects
145. `int` - definite and indefinite integration
146. `int2text` - convert an integer to a character string
147. `irreducible` - test irreducibility of a polynomial
148. `is` - check a mathematical property of an expression
149. `isprime` - primality test
150. `isqrt` - integer square root
151. `iszero` - generic zero test
152. `ithprime` - the i-th prime number
153. `lambertV, lambertW` - lower and upper real branch of the Lambert function
154. `last` - access a previously computed object
155. `lasterror` - reproduce the last error
156. `lcm` - the least common multiple of polynomials
157. `lcoeff` - the leading coefficient of a polynomial
158. `ldegree` - the lowest degree of the terms in a polynomial
159. `length` - the ``length'' of a MuPAD object (heuristic complexity)
160. `level` - evaluate an object with a specified substitution depth
161. `lhs,rhs` - the left, respectively right hand side of equations, inequalities, relations and ranges
162. `limit` - compute a limit
163. `linsolve` - solve a system of linear equations
164. `lllint` - compute an LLL-reduced basis of a lattice
165. `lmonomial` - the leading monomial of a polynomial
166. `ln` - the natural logarithm
167. `loadlib` - load a library package
168. `loadmod` - load a module
169. `loadproc` - load an object on demand
170. `log` - the logarithm to an arbitrary base
171. `lterm` - the leading term of a polynomial
172. `match` - pattern matching
173. `matrix` - create a matrix or a vector
174. `map` - apply a function to all operands of an object
175. `mapcoeffs` - apply a function to the coefficients of a polynomial
176. `maprat` - apply a function to the ``rationalization'' of an expression
177. `max` - the maximum of numbers
178. `min` - the minimum of numbers
179. `mod, modp, mods` - the modulo functions
180. `multcoeffs` - multiply the coefficients of a polynomial with a factor
181. `new` - create a domain element
182. `newDomain` - create a new data type (domain)
183. `next` - skip a step in a loop
184. `nextprime` - the next prime number
185. `nops` - the number of operands
186. `norm` - compute the norm of a matrix, a vector, or a polynomial
187. `normal` - normalize an expression
188. `nterms` - the number of terms of a polynomial
189. `nthcoeff` - the n-th non-zero coefficient of a polynomial
190. `nthmonomial` - the n-th monomial of a polynomial
191. `nthterm` - the n-th term of a polynomial
192. `null` - generate the void object of type `DOM_NULL`
193. `numer` - the numerator of a rational expression
194. `ode` - the domain of ordinary differential equations
195. `op` - the operands of an object
196. `operator` - define a new operator symbol
197. `package` - load a package of new library functions
198. `pade` - Pade approximation
199. `partfrac` - compute a partial fraction decomposition
200. `patchlevel` - the patch number of the installed MuPAD library
201. `pathname` - create a platform dependent path name
202. `pdivide` - pseudo-division of polynomials
203. `piecewise` - the domain of conditionally defined objects
204. `plot` - display graphical objects on the screen
205. `plot2d` - 2D plots
206. `plot3d` - 3D plots
207. `plotfunc2d` - 2D plots of function graphs
208. `plotfunc3d` - 3D plots of function graphs
209. `plotOptions2d` - scene options for 2D plots
210. `plotOptions3d` - scene options for 3D plots
211. `point` - generate a graphical point primitive
212. `poly` - create a polynomial
213. `poly2list` - convert a polynomial to a list of terms
214. `polygon` - generate a graphical polygon primitive
215. `polylog` - the polylogarithm function
216. `powermod` - compute a modular power of a number or a polynomial
217. `print` - print objects to the screen
218. `proc` - define a procedure
219. `product` - definite and indefinite products
220. `protect` - protect an identifier
221. `protocol` - create a protocol of a MuPAD session
222. `psi` - the digamma/polygamma function
223. `quit` - terminate the MuPAD session
224. `radsimp` - simplify radicals in arithmetical expressions
225. `random` - generate random numbers
226. `rationalize` - transform an expression into a rational expression
227. `read` - search, read, and execute a file
228. `repeat, while` - repeat and while loop
229. `rec` - the domain of recurrence equations
230. `rectform` - rectangular form of a complex expression
231. `register` - remove the memory limit of the demo version
232. `reset` - re-initialize a MuPAD session
233. `return` - exit a procedure
234. `revert` - revert lists or character strings, invert series expansions
235. `rewrite` - rewrite an expression
236. `RGB` - predefined color names
237. `select` - select operands
238. `series` - compute a (generalized) series expansion
239. `setuserinfo` - set an information level
240. `share` - create a unique data representation
241. `sign` - the sign of a real or complex number
242. `signIm` - the sign of the imaginary part of a complex number
243. `simplify` - simplify an expression
244. `sin, cos, tan, csc, sec, cot` - the trigonometric functions
245. `sinh, cosh, tanh, csch, sech, coth` - the hyperbolic functions
246. `slot` - method or entry of a domain or a function environment
247. `solve` - solve equations and inequalities
248. `solvers` - an overview of MuPAD's solvers
249. `sort` - sort a list
250. `split` - split an object
251. `sqrt` - the square root function
252. `strmatch` - match a pattern in a character string
253. `subs` - substitute into an object
254. `subsex` - extended substitution
255. `subsop` - replace operands
256. `substring` - extract a substring from a string
257. `sum` - definite and indefinite summation
258. `sysname` - the name of the operating system
259. `sysorder` - compare objects according to the internal order
260. `system` - execute a command of the operating system
261. `table` - create a table
262. `taylor` - compute a Taylor series expansion
263. `tbl2text` - concatenate the strings in a table
264. `tcoeff` - the trailing coefficient of a polynomial
265. `testargs` - decide whether procedure arguments should be tested
266. `testtype` - syntactical type checking
267. `text2expr` - convert a character string to an expression
268. `text2int` - convert a character string to an integer
269. `text2list, text2tbl` - split a character string into substrings
270. `textinput` - interactive input of text
271. `rtime, time` - measure real time and execution time
272. `traperror` - trap errors
273. `type` - the type of an object
274. `unassume` - delete the properties of an identifier
275. `universe` - the set-theoretical universe
276. `unloadmod` - unload a module
277. `unprotect` - remove protection of identifiers
278. `userinfo` - print progress information
279. `val` - the value of an object
280. `version` - the version number of the MuPAD library
281. `warning` - print a warning message
282. `write` - write the values of variables into a file
283. `zeta` - the Riemann zeta function
284. `zip` - combine lists

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