r38_0650.html 32 KB

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  1. <a name=r38_0650>
  2. <title>FPS</title></a>
  3. <p align="centre"><img src="redlogo.gif" width=621 height=60 border=0 alt="REDUC
  4. E"></p>
  5. <b><a href=r38_idx.html>INDEX</a></b><p><p>
  6. <b>FPS</b> _ _ _ _ _ _ _ _ _ _ _ _ <b>package</b><P>
  7. <P>
  8. <P>
  9. <P>
  10. Authors: Wolfram Koepf, Winfried Neun
  11. <P>
  12. <P>
  13. This package can expand a specific class of functions into their
  14. corresponding Laurent-Puiseux series.
  15. <P>
  16. <P>
  17. <a name=r38_0651>
  18. <title>FIDE</title></a>
  19. <p align="centre"><img src="redlogo.gif" width=621 height=60 border=0 alt="REDUC
  20. E"></p>
  21. <b><a href=r38_idx.html>INDEX</a></b><p><p>
  22. <b>FIDE</b> _ _ _ _ _ _ _ _ _ _ _ _ <b>package</b><P>
  23. <P>
  24. Author: Richard Liska
  25. <P>
  26. <P>
  27. This package performs automation of the process of numerically
  28. solving partial differential equations systems (PDES) by means of
  29. computer algebra. For PDES solving, the finite difference method is applied.
  30. The computer algebra system REDUCE and the numerical programming
  31. language FORTRAN are used in the presented methodology. The main aim of
  32. this methodology is to speed up the process of preparing numerical
  33. programs for solving PDES. This process is quite often, especially for
  34. complicated systems, a tedious and time consuming task.
  35. <P>
  36. <P>
  37. <a name=r38_0652>
  38. <title>GENTRAN</title></a>
  39. <p align="centre"><img src="redlogo.gif" width=621 height=60 border=0 alt="REDUC
  40. E"></p>
  41. <b><a href=r38_idx.html>INDEX</a></b><p><p>
  42. <b>GENTRAN</b> _ _ _ _ _ _ _ _ _ _ _ _ <b>package</b><P>
  43. <P>
  44. <P>
  45. <P>
  46. Author: Barbara L. Gates
  47. <P>
  48. <P>
  49. This package is an automatic code GENerator and TRANslator. It constructs
  50. complete numerical programs based on sets of algorithmic specifications and
  51. symbolic expressions. Formatted FORTRAN, RATFOR or C code can be generated
  52. through a series of interactive commands or under the control of a template
  53. processing routine. Large expressions can be automatically segmented into
  54. subexpressions of manageable size, and a special file-handling mechanism
  55. maintains stacks of open I/O channels to allow output to be sent to any
  56. number of files simultaneously and to facilitate recursive invocation of the
  57. whole code generation process.
  58. <P>
  59. <P>
  60. <a name=r38_0653>
  61. <title>IDEALS</title></a>
  62. <p align="centre"><img src="redlogo.gif" width=621 height=60 border=0 alt="REDUC
  63. E"></p>
  64. <b><a href=r38_idx.html>INDEX</a></b><p><p>
  65. <b>IDEALS</b> _ _ _ _ _ _ _ _ _ _ _ _ <b>package</b><P>
  66. <P>
  67. <P>
  68. <P>
  69. Author: Herbert Melenk
  70. <P>
  71. <P>
  72. This package implements the basic arithmetic for polynomial ideals by
  73. exploiting the Groebner bases package of REDUCE. In order to save
  74. computing time all intermediate Groebner bases are stored internally such
  75. that time consuming repetitions are inhibited.
  76. <P>
  77. <P>
  78. <a name=r38_0654>
  79. <title>INEQ</title></a>
  80. <p align="centre"><img src="redlogo.gif" width=621 height=60 border=0 alt="REDUC
  81. E"></p>
  82. <b><a href=r38_idx.html>INDEX</a></b><p><p>
  83. <b>INEQ</b> _ _ _ _ _ _ _ _ _ _ _ _ <b>package</b><P>
  84. <P>
  85. <P>
  86. <P>
  87. Author: Herbert Melenk
  88. <P>
  89. <P>
  90. This package supports the operator <em>ineq_solve</em> that
  91. attempts to solve single inequalities and sets of coupled inequalities.
  92. <P>
  93. <P>
  94. <a name=r38_0655>
  95. <title>INVBASE</title></a>
  96. <p align="centre"><img src="redlogo.gif" width=621 height=60 border=0 alt="REDUC
  97. E"></p>
  98. <b><a href=r38_idx.html>INDEX</a></b><p><p>
  99. <b>INVBASE</b> _ _ _ _ _ _ _ _ _ _ _ _ <b>package</b><P>
  100. <P>
  101. Authors: A.Yu. Zharkov and Yu.A. Blinkov
  102. <P>
  103. <P>
  104. Involutive bases are a new tool for solving problems in connection with
  105. multivariate polynomials, such as solving systems of polynomial equations
  106. and analyzing polynomial ideals. An involutive basis of a polynomial ideal
  107. is nothing more than a special form of a redundant Groebner basis. The
  108. construction of involutive bases reduces the problem of solving polynomial
  109. systems to simple linear algebra.
  110. <P>
  111. <P>
  112. <a name=r38_0656>
  113. <title>LAPLACE</title></a>
  114. <p align="centre"><img src="redlogo.gif" width=621 height=60 border=0 alt="REDUC
  115. E"></p>
  116. <b><a href=r38_idx.html>INDEX</a></b><p><p>
  117. <b>LAPLACE</b> _ _ _ _ _ _ _ _ _ _ _ _ <b>package</b><P>
  118. <P>
  119. <P>
  120. <P>
  121. Authors: C. Kazasov, M. Spiridonova, V. Tomov
  122. <P>
  123. <P>
  124. This package can calculate ordinary and inverse Laplace transforms of
  125. expressions.
  126. <P>
  127. <P>
  128. <a name=r38_0657>
  129. <title>LIE</title></a>
  130. <p align="centre"><img src="redlogo.gif" width=621 height=60 border=0 alt="REDUC
  131. E"></p>
  132. <b><a href=r38_idx.html>INDEX</a></b><p><p>
  133. <b>LIE</b> _ _ _ _ _ _ _ _ _ _ _ _ <b>package</b><P>
  134. <P>
  135. Authors: Carsten and Franziska Sch&quot;obel
  136. <P>
  137. <P>
  138. <em>Lie</em>is a package of functions for the classification of real
  139. n-dimensional Lie algebras. It consists of two modules: <em>liendmc1</em>
  140. and <em>lie1234</em>. With the help of the functions in the <em>liendmcl</em>
  141. module, real n-dimensional Lie algebras L with a derived algebra
  142. L^(1) of dimension 1 can be classified.
  143. <P>
  144. <P>
  145. <a name=r38_0658>
  146. <title>MODSR</title></a>
  147. <p align="centre"><img src="redlogo.gif" width=621 height=60 border=0 alt="REDUC
  148. E"></p>
  149. <b><a href=r38_idx.html>INDEX</a></b><p><p>
  150. <b>MODSR</b> _ _ _ _ _ _ _ _ _ _ _ _ <b>package</b><P>
  151. <P>
  152. <P>
  153. <P>
  154. Author: Herbert Melenk
  155. <P>
  156. <P>
  157. This package supports solve (M_SOLVE) and roots (M_ROOTS) operators for
  158. modular polynomials and modular polynomial systems. The moduli need not
  159. be primes. M_SOLVE requires a modulus to be set. M_ROOTS takes the
  160. modulus as a second argument. For example:
  161. <P>
  162. <P>
  163. <p><pre><tt>
  164. on modular; setmod 8;
  165. m_solve(2x=4); -&gt; {{X=2},{X=6}}
  166. m_solve({x^2-y^3=3});
  167. -&gt; {{X=0,Y=5}, {X=2,Y=1}, {X=4,Y=5}, {X=6,Y=1}}
  168. m_solve({x=2,x^2-y^3=3}); -&gt; {{X=2,Y=1}}
  169. off modular;
  170. m_roots(x^2-1,8); -&gt; {1,3,5,7}
  171. m_roots(x^3-x,7); -&gt; {0,1,6}
  172. </tt></pre><p>
  173. <a name=r38_0659>
  174. <title>NCPOLY</title></a>
  175. <p align="centre"><img src="redlogo.gif" width=621 height=60 border=0 alt="REDUC
  176. E"></p>
  177. <b><a href=r38_idx.html>INDEX</a></b><p><p>
  178. <b>NCPOLY</b> _ _ _ _ _ _ _ _ _ _ _ _ <b>package</b><P>
  179. <P>
  180. <P>
  181. <P>
  182. Authors: Herbert Melenk, Joachim Apel
  183. <P>
  184. <P>
  185. This package allows the user to set up automatically a consistent
  186. environment for computing in an algebra where the non--commutativity is
  187. defined by Lie-bracket commutators. The package uses the REDUCE
  188. <em>noncom</em> mechanism for elementary polynomial arithmetic; the commutator
  189. rules are automatically computed from the Lie brackets.
  190. <P>
  191. <P>
  192. <a name=r38_0660>
  193. <title>ORTHOVEC</title></a>
  194. <p align="centre"><img src="redlogo.gif" width=621 height=60 border=0 alt="REDUC
  195. E"></p>
  196. <b><a href=r38_idx.html>INDEX</a></b><p><p>
  197. <b>ORTHOVEC</b> _ _ _ _ _ _ _ _ _ _ _ _ <b>package</b><P>
  198. <P>
  199. <P>
  200. <P>
  201. Author: James W. Eastwood
  202. <P>
  203. <P>
  204. <em>orthovec</em>is a collection of REDUCE procedures and operations which
  205. provide a simple-to-use environment for the manipulation of scalars and
  206. vectors. Operations include addition, subtraction, dot and cross
  207. products, division, modulus, div, grad, curl, laplacian, differentiation,
  208. integration, and Taylor expansion.
  209. <P>
  210. <P>
  211. <a name=r38_0661>
  212. <title>PHYSOP</title></a>
  213. <p align="centre"><img src="redlogo.gif" width=621 height=60 border=0 alt="REDUC
  214. E"></p>
  215. <b><a href=r38_idx.html>INDEX</a></b><p><p>
  216. <b>PHYSOP</b> _ _ _ _ _ _ _ _ _ _ _ _ <b>package</b><P>
  217. <P>
  218. Author: Mathias Warns
  219. <P>
  220. <P>
  221. This package has been designed to meet the requirements of theoretical
  222. physicists looking for a computer algebra tool to perform complicated
  223. calculations in quantum theory with expressions containing operators.
  224. These operations consist mainly of the calculation of commutators between
  225. operator expressions and in the evaluations of operator matrix elements in
  226. some abstract space.
  227. <P>
  228. <P>
  229. <a name=r38_0662>
  230. <title>PM</title></a>
  231. <p align="centre"><img src="redlogo.gif" width=621 height=60 border=0 alt="REDUC
  232. E"></p>
  233. <b><a href=r38_idx.html>INDEX</a></b><p><p>
  234. <b>PM</b> _ _ _ _ _ _ _ _ _ _ _ _ <b>package</b><P>
  235. <P>
  236. <P>
  237. <P>
  238. Author: Kevin McIsaac
  239. <P>
  240. <P>
  241. PM is a general pattern matcher similar in style to those found in systems
  242. such as SMP and Mathematica, and is based on the pattern matcher described
  243. in Kevin McIsaac, ``Pattern Matching Algebraic Identities'', SIGSAM Bulletin,
  244. 19 (1985), 4-13.
  245. <P>
  246. <P>
  247. <a name=r38_0663>
  248. <title>RANDPOLY</title></a>
  249. <p align="centre"><img src="redlogo.gif" width=621 height=60 border=0 alt="REDUC
  250. E"></p>
  251. <b><a href=r38_idx.html>INDEX</a></b><p><p>
  252. <b>RANDPOLY</b> _ _ _ _ _ _ _ _ _ _ _ _ <b>package</b><P>
  253. <P>
  254. <P>
  255. <P>
  256. Author: Francis J. Wright
  257. <P>
  258. <P>
  259. This package is based on a port of the Maple random polynomial
  260. generator together with some support facilities for the generation
  261. of random numbers and anonymous procedures.
  262. <P>
  263. <P>
  264. <a name=r38_0664>
  265. <title>REACTEQN</title></a>
  266. <p align="centre"><img src="redlogo.gif" width=621 height=60 border=0 alt="REDUC
  267. E"></p>
  268. <b><a href=r38_idx.html>INDEX</a></b><p><p>
  269. <b>REACTEQN</b> _ _ _ _ _ _ _ _ _ _ _ _ <b>package</b><P>
  270. <P>
  271. <P>
  272. <P>
  273. Author: Herbert Melenk
  274. <P>
  275. <P>
  276. This package allows a user to transform chemical reaction systems into
  277. ordinary differential equation systems (ODE) corresponding to the laws of
  278. pure mass action.
  279. <P>
  280. <P>
  281. <a name=r38_0665>
  282. <title>RESET</title></a>
  283. <p align="centre"><img src="redlogo.gif" width=621 height=60 border=0 alt="REDUC
  284. E"></p>
  285. <b><a href=r38_idx.html>INDEX</a></b><p><p>
  286. <b>RESET</b> _ _ _ _ _ _ _ _ _ _ _ _ <b>package</b><P>
  287. <P>
  288. Author: John Fitch
  289. <P>
  290. <P>
  291. This package defines a command command RESETREDUCE that works through the
  292. history of previous commands, and clears any values which have been
  293. assigned, plus any rules, arrays and the like. It also sets the various
  294. switches to their initial values. It is not complete, but does work for
  295. most things that cause a gradual loss of space. It would be relatively
  296. easy to make it interactive, so allowing for selective resetting.
  297. <P>
  298. <P>
  299. <a name=r38_0666>
  300. <title>RESIDUE</title></a>
  301. <p align="centre"><img src="redlogo.gif" width=621 height=60 border=0 alt="REDUC
  302. E"></p>
  303. <b><a href=r38_idx.html>INDEX</a></b><p><p>
  304. <b>RESIDUE</b> _ _ _ _ _ _ _ _ _ _ _ _ <b>package</b><P>
  305. <P>
  306. Author: Wolfram Koepf
  307. <P>
  308. <P>
  309. This package supports the calculation of residues of arbitrary
  310. expressions.
  311. <P>
  312. <P>
  313. <a name=r38_0667>
  314. <title>RLFI</title></a>
  315. <p align="centre"><img src="redlogo.gif" width=621 height=60 border=0 alt="REDUC
  316. E"></p>
  317. <b><a href=r38_idx.html>INDEX</a></b><p><p>
  318. <b>RLFI</b> _ _ _ _ _ _ _ _ _ _ _ _ <b>package</b><P>
  319. <P>
  320. <P>
  321. <P>
  322. Author: Richard Liska
  323. <P>
  324. <P>
  325. This package
  326. adds LaTeX syntax
  327. to REDUCE. Text generated by REDUCE in this mode can be directly
  328. used in LaTeX source
  329. documents. Various
  330. mathematical constructions are supported by the interface including
  331. subscripts, superscripts, font changing, Greek letters, divide-bars,
  332. integral and sum signs, derivatives, and so on.
  333. <P>
  334. <P>
  335. <a name=r38_0668>
  336. <title>SCOPE</title></a>
  337. <p align="centre"><img src="redlogo.gif" width=621 height=60 border=0 alt="REDUC
  338. E"></p>
  339. <b><a href=r38_idx.html>INDEX</a></b><p><p>
  340. <b>SCOPE</b> _ _ _ _ _ _ _ _ _ _ _ _ <b>package</b><P>
  341. <P>
  342. <P>
  343. <P>
  344. Author: J.A. van Hulzen
  345. <P>
  346. <P>
  347. SCOPE is a package for the production of an optimized form of a set of
  348. expressions. It applies an heuristic search for common (sub)expressions
  349. to almost any set of proper REDUCE assignment statements. The output is
  350. obtained as a sequence of assignment statements. <em>gentran</em> is used to
  351. facilitate expression output.
  352. <P>
  353. <P>
  354. <a name=r38_0669>
  355. <title>SETS</title></a>
  356. <p align="centre"><img src="redlogo.gif" width=621 height=60 border=0 alt="REDUC
  357. E"></p>
  358. <b><a href=r38_idx.html>INDEX</a></b><p><p>
  359. <b>SETS</b> _ _ _ _ _ _ _ _ _ _ _ _ <b>package</b><P>
  360. <P>
  361. Author: Francis J. Wright
  362. <P>
  363. <P>
  364. The SETS package provides algebraic-mode support for set operations on
  365. lists regarded as sets (or representing explicit sets) and on implicit
  366. sets represented by identifiers.
  367. <P>
  368. <P>
  369. <a name=r38_0670>
  370. <title>SPDE</title></a>
  371. <p align="centre"><img src="redlogo.gif" width=621 height=60 border=0 alt="REDUC
  372. E"></p>
  373. <b><a href=r38_idx.html>INDEX</a></b><p><p>
  374. <b>SPDE</b> _ _ _ _ _ _ _ _ _ _ _ _ <b>package</b><P>
  375. <P>
  376. <P>
  377. <P>
  378. Author: Fritz Schwartz
  379. <P>
  380. <P>
  381. The package <em>spde</em> provides a set of functions which may be used to
  382. determine the symmetry group of Lie- or point-symmetries of a given system of
  383. partial differential equations. In many cases the determining system is
  384. solved completely automatically. In other cases the user has to provide
  385. additional input information for the solution algorithm to terminate.
  386. <P>
  387. <P>
  388. <a name=r38_0671>
  389. <title>SYMMETRY</title></a>
  390. <p align="centre"><img src="redlogo.gif" width=621 height=60 border=0 alt="REDUC
  391. E"></p>
  392. <b><a href=r38_idx.html>INDEX</a></b><p><p>
  393. <b>SYMMETRY</b> _ _ _ _ _ _ _ _ _ _ _ _ <b>package</b><P>
  394. <P>
  395. Author: Karin Gatermann
  396. <P>
  397. <P>
  398. This package computes symmetry-adapted bases and block diagonal forms of
  399. matrices which have the symmetry of a group. The package is the
  400. implementation of the theory of linear representations for small finite
  401. groups such as the dihedral groups.
  402. <P>
  403. <P>
  404. <a name=r38_0672>
  405. <title>TPS</title></a>
  406. <p align="centre"><img src="redlogo.gif" width=621 height=60 border=0 alt="REDUC
  407. E"></p>
  408. <b><a href=r38_idx.html>INDEX</a></b><p><p>
  409. <b>TPS</b> _ _ _ _ _ _ _ _ _ _ _ _ <b>package</b><P>
  410. <P>
  411. <P>
  412. <P>
  413. Authors: Alan Barnes, Julian Padget
  414. <P>
  415. <P>
  416. This package implements formal Laurent series expansions in one variable
  417. using the domain mechanism of REDUCE. This means that power series
  418. objects can be added, multiplied, differentiated etc., like other first
  419. class objects in the system. A lazy evaluation scheme is used and thus
  420. terms of the series are not evaluated until they are required for printing
  421. or for use in calculating terms in other power series. The series are
  422. extendible giving the user the impression that the full infinite series is
  423. being manipulated. The errors that can sometimes occur using series that
  424. are truncated at some fixed depth (for example when a term in the required
  425. series depends on terms of an intermediate series beyond the truncation
  426. depth) are thus avoided.
  427. <P>
  428. <P>
  429. <a name=r38_0673>
  430. <title>TRI</title></a>
  431. <p align="centre"><img src="redlogo.gif" width=621 height=60 border=0 alt="REDUC
  432. E"></p>
  433. <b><a href=r38_idx.html>INDEX</a></b><p><p>
  434. <b>TRI</b> _ _ _ _ _ _ _ _ _ _ _ _ <b>package</b><P>
  435. <P>
  436. <P>
  437. <P>
  438. Author: Werner Antweiler
  439. <P>
  440. <P>
  441. This package provides facilities written in REDUCE-Lisp for typesetting
  442. REDUCE formulas
  443. using TeX. The
  444. TeX-REDUCE-Interface incorporates three levels
  445. of TeX output:
  446. without line breaking, with line breaking, and
  447. with line breaking plus indentation.
  448. <P>
  449. <P>
  450. <a name=r38_0674>
  451. <title>TRIGSIMP</title></a>
  452. <p align="centre"><img src="redlogo.gif" width=621 height=60 border=0 alt="REDUC
  453. E"></p>
  454. <b><a href=r38_idx.html>INDEX</a></b><p><p>
  455. <b>TRIGSIMP</b> _ _ _ _ _ _ _ _ _ _ _ _ <b>package</b><P>
  456. <P>
  457. <P>
  458. <P>
  459. Author: Wolfram Koepf
  460. <P>
  461. <P>
  462. TRIGSIMP is a useful tool for all kinds of trigonometric and hyperbolic
  463. simplification and factorization. There are three procedures included in
  464. TRIGSIMP: <em>trigsimp</em>, <em>trigfactorize</em> and <em>triggcd</em>. The
  465. first is for finding simplifications of trigonometric or hyperbolic
  466. expressions with many options, the second for factorizing them and the
  467. third for finding the greatest common divisor of two trigonometric or
  468. hyperbolic polynomials.
  469. <P>
  470. <P>
  471. <a name=r38_0675>
  472. <title>XCOLOR</title></a>
  473. <p align="centre"><img src="redlogo.gif" width=621 height=60 border=0 alt="REDUC
  474. E"></p>
  475. <b><a href=r38_idx.html>INDEX</a></b><p><p>
  476. <b>XCOLOR</b> _ _ _ _ _ _ _ _ _ _ _ _ <b>package</b><P>
  477. <P>
  478. <P>
  479. <P>
  480. Author: A. Kryukov
  481. <P>
  482. <P>
  483. This package calculates the color factor in non-abelian gauge field
  484. theories using an algorithm due to Cvitanovich.
  485. <P>
  486. <P>
  487. <a name=r38_0676>
  488. <title>XIDEAL</title></a>
  489. <p align="centre"><img src="redlogo.gif" width=621 height=60 border=0 alt="REDUC
  490. E"></p>
  491. <b><a href=r38_idx.html>INDEX</a></b><p><p>
  492. <b>XIDEAL</b> _ _ _ _ _ _ _ _ _ _ _ _ <b>package</b><P>
  493. <P>
  494. <P>
  495. <P>
  496. Author: David Hartley
  497. <P>
  498. <P>
  499. <em>xideal</em>constructs Groebner bases for solving the left ideal
  500. membership problem: Groebner left ideal bases or GLIBs. For graded
  501. ideals, where each form is homogeneous in degree, the distinction between
  502. left and right ideals vanishes. Furthermore, if the generating forms are
  503. all homogeneous, then the Groebner bases for the non-graded and graded
  504. ideals are identical. In this case, <em>xideal</em> is able to save time by
  505. truncating the Groebner basis at some maximum degree if desired.
  506. <P>
  507. <P>
  508. <a name=r38_0677>
  509. <title>WU</title></a>
  510. <p align="centre"><img src="redlogo.gif" width=621 height=60 border=0 alt="REDUC
  511. E"></p>
  512. <b><a href=r38_idx.html>INDEX</a></b><p><p>
  513. <b>WU</b> _ _ _ _ _ _ _ _ _ _ _ _ <b>package</b><P>
  514. <P>
  515. <P>
  516. <P>
  517. Author: Russell Bradford
  518. <P>
  519. <P>
  520. This is a simple implementation of the Wu algorithm implemented in REDUCE
  521. working directly from ``A Zero Structure Theorem for
  522. Polynomial-Equations-Solving,'' Wu Wen-tsun, Institute of Systems Science,
  523. Academia Sinica, Beijing.
  524. <P>
  525. <P>
  526. <a name=r38_0678>
  527. <title>ZEILBERG</title></a>
  528. <p align="centre"><img src="redlogo.gif" width=621 height=60 border=0 alt="REDUC
  529. E"></p>
  530. <b><a href=r38_idx.html>INDEX</a></b><p><p>
  531. <b>ZEILBERG</b> _ _ _ _ _ _ _ _ _ _ _ _ <b>package</b><P>
  532. <P>
  533. <P>
  534. <P>
  535. Authors: Gregor St&quot;olting and Wolfram Koepf
  536. <P>
  537. <P>
  538. This package is a careful implementation of the Gosper and Zeilberger
  539. algorithms for indefinite and definite summation of hypergeometric terms,
  540. respectively. Extensions of these algorithms are also included that are
  541. valid for ratios of products of powers,
  542. factorials, gamma function
  543. terms, binomial coefficients, and shifted factorials that are
  544. rational-linear in their arguments.
  545. <P>
  546. <P>
  547. <a name=r38_0679>
  548. <title>ZTRANS</title></a>
  549. <p align="centre"><img src="redlogo.gif" width=621 height=60 border=0 alt="REDUC
  550. E"></p>
  551. <b><a href=r38_idx.html>INDEX</a></b><p><p>
  552. <b>ZTRANS</b> _ _ _ _ _ _ _ _ _ _ _ _ <b>package</b><P>
  553. <P>
  554. Authors: Wolfram Koepf, Lisa Temme
  555. <P>
  556. <P>
  557. This package is an implementation of the Z-transform of a sequence.
  558. This is the discrete analogue of the Laplace Transform.
  559. <P>
  560. <P>
  561. <a name=r38_0680>
  562. <title>Miscellaneous Packages</title></a>
  563. <p align="centre"><img src="redlogo.gif" width=621 height=60 border=0 alt="REDUC
  564. E"></p>
  565. <b><a href=r38_idx.html>INDEX</a></b><p><p>
  566. <b>Miscellaneous Packages</b><menu>
  567. <li><a href=r38_0600.html#r38_0632>Miscellaneous Packages introduction</a><P>
  568. <li><a href=r38_0600.html#r38_0633>ALGINT package</a><P>
  569. <li><a href=r38_0600.html#r38_0634>APPLYSYM package</a><P>
  570. <li><a href=r38_0600.html#r38_0635>ARNUM package</a><P>
  571. <li><a href=r38_0600.html#r38_0636>ASSIST package</a><P>
  572. <li><a href=r38_0600.html#r38_0637>AVECTOR package</a><P>
  573. <li><a href=r38_0600.html#r38_0638>BOOLEAN package</a><P>
  574. <li><a href=r38_0600.html#r38_0639>CALI package</a><P>
  575. <li><a href=r38_0600.html#r38_0640>CAMAL package</a><P>
  576. <li><a href=r38_0600.html#r38_0641>CHANGEVR package</a><P>
  577. <li><a href=r38_0600.html#r38_0642>COMPACT package</a><P>
  578. <li><a href=r38_0600.html#r38_0643>CRACK package</a><P>
  579. <li><a href=r38_0600.html#r38_0644>CVIT package</a><P>
  580. <li><a href=r38_0600.html#r38_0645>DEFINT package</a><P>
  581. <li><a href=r38_0600.html#r38_0646>DESIR package</a><P>
  582. <li><a href=r38_0600.html#r38_0647>DFPART package</a><P>
  583. <li><a href=r38_0600.html#r38_0648>DUMMY package</a><P>
  584. <li><a href=r38_0600.html#r38_0649>EXCALC package</a><P>
  585. <li><a href=r38_0650.html#r38_0650>FPS package</a><P>
  586. <li><a href=r38_0650.html#r38_0651>FIDE package</a><P>
  587. <li><a href=r38_0650.html#r38_0652>GENTRAN package</a><P>
  588. <li><a href=r38_0650.html#r38_0653>IDEALS package</a><P>
  589. <li><a href=r38_0650.html#r38_0654>INEQ package</a><P>
  590. <li><a href=r38_0650.html#r38_0655>INVBASE package</a><P>
  591. <li><a href=r38_0650.html#r38_0656>LAPLACE package</a><P>
  592. <li><a href=r38_0650.html#r38_0657>LIE package</a><P>
  593. <li><a href=r38_0650.html#r38_0658>MODSR package</a><P>
  594. <li><a href=r38_0650.html#r38_0659>NCPOLY package</a><P>
  595. <li><a href=r38_0650.html#r38_0660>ORTHOVEC package</a><P>
  596. <li><a href=r38_0650.html#r38_0661>PHYSOP package</a><P>
  597. <li><a href=r38_0650.html#r38_0662>PM package</a><P>
  598. <li><a href=r38_0650.html#r38_0663>RANDPOLY package</a><P>
  599. <li><a href=r38_0650.html#r38_0664>REACTEQN package</a><P>
  600. <li><a href=r38_0650.html#r38_0665>RESET package</a><P>
  601. <li><a href=r38_0650.html#r38_0666>RESIDUE package</a><P>
  602. <li><a href=r38_0650.html#r38_0667>RLFI package</a><P>
  603. <li><a href=r38_0650.html#r38_0668>SCOPE package</a><P>
  604. <li><a href=r38_0650.html#r38_0669>SETS package</a><P>
  605. <li><a href=r38_0650.html#r38_0670>SPDE package</a><P>
  606. <li><a href=r38_0650.html#r38_0671>SYMMETRY package</a><P>
  607. <li><a href=r38_0650.html#r38_0672>TPS package</a><P>
  608. <li><a href=r38_0650.html#r38_0673>TRI package</a><P>
  609. <li><a href=r38_0650.html#r38_0674>TRIGSIMP package</a><P>
  610. <li><a href=r38_0650.html#r38_0675>XCOLOR package</a><P>
  611. <li><a href=r38_0650.html#r38_0676>XIDEAL package</a><P>
  612. <li><a href=r38_0650.html#r38_0677>WU package</a><P>
  613. <li><a href=r38_0650.html#r38_0678>ZEILBERG package</a><P>
  614. <li><a href=r38_0650.html#r38_0679>ZTRANS package</a><P>
  615. </menu>
  616. <a name=r38_0681>
  617. <title>ED</title></a>
  618. <p align="centre"><img src="redlogo.gif" width=621 height=60 border=0 alt="REDUC
  619. E"></p>
  620. <b><a href=r38_idx.html>INDEX</a></b><p><p>
  621. <b>ED</b> _ _ _ _ _ _ _ _ _ _ _ _ <b>command</b><P>
  622. <P>
  623. The <em>ed</em> command invokes a simple line editor for REDUCE input
  624. statements.
  625. <P>
  626. <P>
  627. <P> <H3>
  628. syntax: </H3>
  629. <em>ed</em>&lt;integer&gt; or <em>ed</em>
  630. <P>
  631. <P>
  632. <P>
  633. <em>ed</em>called with no argument edits the last input statement. If
  634. &lt;integer&gt; is greater than or equal to the current line number, an error
  635. message is printed. Reenter a proper <em>ed</em> command or return to the
  636. top level with a semicolon.
  637. <P>
  638. <P>
  639. The editor formats REDUCE's version of the desired input statement,
  640. dividing it into lines at semicolons and dollar signs. The statement is
  641. printed at the beginning of the edit session. The editor works on one
  642. line at a time, and has a pointer (shown by <em>^</em>) to the current
  643. character of that line. When the session begins, the pointer is at the
  644. left hand side of the first line. The editing prompt is <em>&gt;</em>.
  645. <P>
  646. <P>
  647. The following commands are available. They may be entered in either upper
  648. or lower case. All commands are activated by the carriage return, which
  649. also prints out the current line after changes. Several commands can be
  650. placed on a single line, except that commands terminated by an <em>ESC</em>
  651. must be the last command before the carriage return.
  652. <P>
  653. <P>
  654. _ _ _ b
  655. Move pointer to beginning of current line.
  656. <P>
  657. <P>
  658. _ _ _ d&lt;digit&gt;
  659. Delete current character and next (digit-1) characters. An error message
  660. is printed if anything other than a single digit follows d. If there are
  661. fewer than &lt;digit&gt; characters left on the line, all but the final
  662. dollar sign or semicolon is removed. To delete a line completely, use the
  663. k command.
  664. <P>
  665. <P>
  666. _ _ _ e
  667. End the current session, causing the edited expression to be reparsed by
  668. REDUCE.
  669. <P>
  670. <P>
  671. _ _ _ f&lt;char&gt;
  672. Find the next occurrence of the character &lt;char&gt; to the right of the
  673. pointer on the current line and move the pointer to it. If the character is
  674. not found, an error message is printed and the pointer remains in its
  675. original position. Other lines are not searched. The f command is not
  676. case-sensitive.
  677. <P>
  678. <P>
  679. _ _ _ i&lt;string&gt;<em>ESC</em>
  680. Insert &lt;string&gt; in front of pointer. The <em>ESC</em> key is your
  681. delimiter for the input string. No other command may follow this one on
  682. the same line.
  683. <P>
  684. <P>
  685. _ _ _ k
  686. Kill rest of the current line, including the semicolon or dollar sign
  687. terminator. If there are characters remaining on the current line, and it
  688. is the last line of the input statement, a semicolon is added to the line
  689. as a terminator for REDUCE. If the current line is now empty, one of the
  690. following actions is performed: If there is a following line, it becomes
  691. the current line and the pointer is placed at its first character. If the
  692. current line was the final line of the statement, and there is a previous
  693. line, the previous line becomes the current line. If the current line was
  694. the only line of the statement, and it is empty, a single semicolon is
  695. inserted for REDUCE to parse.
  696. <P>
  697. <P>
  698. _ _ _ l
  699. Finish editing this line and move to the last previous line. An error message
  700. is printed if there is no previous line.
  701. <P>
  702. <P>
  703. _ _ _ n
  704. Finish editing this line and move to the next line. An error message is
  705. printed if there is no next line.
  706. <P>
  707. <P>
  708. _ _ _ p
  709. Print out all the lines of the statement. Then a dotted line is printed, and
  710. the current line is reprinted, with the pointer under it.
  711. <P>
  712. <P>
  713. _ _ _ q
  714. Quit the editing session without saving the changes. If a semicolon is
  715. entered after q, a new line prompt is given, otherwise REDUCE prompts you
  716. for another command. Whatever you type in to the prompt appearing after
  717. the q is entered is stored as the input for the line number in which you
  718. called the edit. Thus if you enter a semicolon, neither
  719. <a href=r38_0200.html#r38_0232>input</a>
  720. <em>ed</em> will find anything under the current number.
  721. <P>
  722. <P>
  723. _ _ _ r&lt;char&gt;
  724. Replace the character at the pointer by &lt;char&gt;.
  725. <P>
  726. <P>
  727. _ _ _ s&lt;string&gt;<em>ESC</em>
  728. Search for the first occurrence of &lt;string&gt; to the right of the
  729. pointer on the current line and move the pointer to its first character.
  730. The <em>ESC</em> key is your delimiter for the input string. The s function
  731. does not search other lines of the statement. If the string is not found,
  732. an error message is printed and the pointer remains in its original
  733. position. The s command is not case-sensitive. No other command may
  734. follow this one on the same line.
  735. <P>
  736. <P>
  737. _ _ _ x &lt;or space&gt;
  738. Move the pointer one character to the right. If the pointer is already at
  739. the end of the line, an error message is printed.
  740. <P>
  741. <P>
  742. _ _ _ - &lt;(minus)&gt;
  743. Move the pointer one character to the left. If the pointer is already at the
  744. beginning of the line, an error message is printed.
  745. <P>
  746. <P>
  747. _ _ _ ?
  748. Display the Help menu, showing the commands and their actions.
  749. <P>
  750. <P>
  751. <P> <H3>
  752. examples: </H3>
  753. <p><pre><tt></tt></pre><p>(Line numbers are shown in the following examples)<p>
  754. <pre><tt>
  755. 2: &gt;&gt;x**2 + y;
  756. X^{2} + Y
  757. 3: &gt;&gt;ed 2;
  758. X**2 + Y;
  759. ^
  760. For help, type '?'
  761. ?- (Enter three spaces and key{Return})
  762. X**2 + Y;
  763. ^
  764. ?- r5
  765. X**5 + Y;
  766. ^
  767. ?- fY
  768. X**5 + Y;
  769. ^
  770. ?- iabc (Terminate with key{ESC} and key{Return})
  771. X**5 + abcY;
  772. ^
  773. ?- ----
  774. X**5 + abcY;
  775. ^
  776. ?- fbd2
  777. X**5 + aY;
  778. ^
  779. ?- b
  780. X**5 + aY;
  781. ^
  782. ?- e
  783. AY + X^{5}
  784. 4: &gt;&gt;procedure dumb(a);
  785. &gt;&gt;write a;
  786. DUMB
  787. 5: &gt;&gt;dumb(17);
  788. 17
  789. 6: &gt;&gt;ed 4;
  790. PROCEDURE DUMB (A);
  791. ^
  792. WRITE A;
  793. ?- fArBn
  794. WRITE A;
  795. ^
  796. ?- ibegin scalar a; a := b + 10; (Type a space, key{ESC}, and key{Return})
  797. begin scalar a; a := b + 10; WRITE A;
  798. ?- f;i end key{ESC}, key{Return}
  799. begin scalar b; b := a + 10; WRITE A end;
  800. ^
  801. ?- p
  802. PROCEDURE DUMB (B);
  803. begin scalar b; b := a + 10; WRITE A end;
  804. - - - - - - - - - -
  805. begin scalar b; b := a + 10; WRITE A end;
  806. ^
  807. ?- e
  808. DUMB
  809. 7: &gt;&gt;dumb(17);
  810. 27
  811. 8: &gt;&gt;
  812. </tt></pre><p>
  813. <P>
  814. <P>
  815. Note that REDUCE reparsed the procedure <em>dumb</em> and updated the
  816. definition.
  817. <P>
  818. <P>
  819. Since REDUCE divides the expression to be edited into lines at semicolons or
  820. dollar sign terminators, some lines may occupy more than one line of screen
  821. space. If the pointer is directly beneath the last line of text, it
  822. refers to the top line of text. If there is a blank line between the
  823. last line of text and the pointer, it refers to the second line
  824. of text, and likewise for cases of greater than two lines of text. In other
  825. words, the entire REDUCE statement up to the next terminator is printed, even
  826. if it runs to several lines, then the pointer line is printed.
  827. <P>
  828. <P>
  829. You can insert new statements which contain semicolons of their own into the
  830. current line. They are run into the current line where you placed them
  831. until you edit the statement again. REDUCE will understand the set of
  832. statements if the syntax is correct.
  833. <P>
  834. <P>
  835. If you leave out needed closing brackets when you exit the editor, a message
  836. is printed allowing you to redo the edit (you can edit the previous line
  837. number and return to where you were). If you leave out a closing
  838. double-quotation mark, an error message is printed, and the editing must be
  839. redone from the original version; the edited version has been destroyed.
  840. Most syntax errors which you inadvertently leave in an edited statement are
  841. caught as usual by the REDUCE parser, and you will be able to re-edit the
  842. statement.
  843. <P>
  844. <P>
  845. When the editor processes a previous statement for your editing, escape
  846. characters are removed. Most special characters that you may use in
  847. identifiers are printed in legal fashion, prefixed by the exclamation
  848. point. Be sure to treat the special character and its escape as a pair in
  849. your editing. The characters <em>( ) # ; ' `</em> are different. Since
  850. they have special meaning in Lisp, they are double-escaped in the editor.
  851. It is unwise to use these characters inside identifiers anyway, due to the
  852. probability of confusion.
  853. <P>
  854. <P>
  855. If you see a Lisp error message during editing, the edit has been aborted.
  856. Enter a semicolon and you will see a new line prompt.
  857. <P>
  858. <P>
  859. Since the editor has no dependence on any window system, it can be used if you
  860. are running REDUCE without windows.
  861. <P>
  862. <P>
  863. <P>
  864. <a name=r38_0682>
  865. <title>EDITDEF</title></a>
  866. <p align="centre"><img src="redlogo.gif" width=621 height=60 border=0 alt="REDUC
  867. E"></p>
  868. <b><a href=r38_idx.html>INDEX</a></b><p><p>
  869. <b>EDITDEF</b> _ _ _ _ _ _ _ _ _ _ _ _ <b>command</b><P>
  870. <P>
  871. <P>
  872. <P>
  873. The interactive editor
  874. <a href=r38_0650.html#r38_0681>ed</a> may be used to edit a user-defined
  875. procedure that has not been compiled.
  876. <P> <H3>
  877. syntax: </H3>
  878. <P>
  879. <P>
  880. <em>editdef</em>(<em>identifier</em>)
  881. <P>
  882. <P>
  883. <P>
  884. where <em>identifier</em> is the name of the procedure. When <em>editdef</em>
  885. is invoked, the procedure definition will be displayed in editing mode,
  886. and may then be edited and redefined on exiting from the editor using
  887. standard
  888. <a href=r38_0650.html#r38_0681>ed</a> commands.
  889. <P>
  890. <P>
  891. <a name=r38_0683>
  892. <title>Outmoded Operations</title></a>
  893. <p align="centre"><img src="redlogo.gif" width=621 height=60 border=0 alt="REDUC
  894. E"></p>
  895. <b><a href=r38_idx.html>INDEX</a></b><p><p>
  896. <b>Outmoded Operations</b><menu>
  897. <li><a href=r38_0650.html#r38_0681>ED command</a><P>
  898. <li><a href=r38_0650.html#r38_0682>EDITDEF command</a><P>
  899. </menu>