2065:
2077:
1242:
880:
1237:{\displaystyle {\begin{cases}{\begin{aligned}f(x,y,z)&=xy+z\\p&=x+y\\q&=x-y\\r&=x^{2}+y^{2}\\f(p,q,r)&=pq+r\\&=(x+y)(x-y)+x^{2}+y^{2}\\&=(x^{2}-y^{2})+x^{2}+y^{2}\\&=2x^{2}\end{aligned}}\end{cases}}}
1360:
135:
computers, on which ALPAK and ALTRAN were reliant, began to be phased out in favor of newer machines. This led to development of a more advanced ALTRAN language and implementation developed by Brown, Andrew D. Hall,
1733:
It is clear that the degree of portability promised cannot approach that of ALTRAN, for example, which can be brought up with a fortnight of effort by someone skilled in local conditions but ignorant of ALTRAN
1478:
155:
Later, Feldman and Julia Ho added a rational expression evaluation package that generated accurate and efficient FORTRAN subroutines for the numerical evaluation of symbolic expressions produced by ALTRAN.
1781:
W.S. Brown, "A language and system for symbolic algebra on a digital computer", SYMSAC '66 Proceedings of the first ACM symposium on
Symbolic and algebraic manipulation, p. 501- 540, January 1966.
864:
893:
750:
663:
579:
509:
101:
Although ALTRAN is written in ANSI FORTRAN, nevertheless there exist differences in FORTRAN implementations. ALTRAN handles machine dependencies through the use of a
186:." It was also observed that ALTRAN was able to quickly solve problems which neither FORMAC nor REDUCE could handle on the given hardware or in reasonable time.
1796:
Mansour Farah, "A FORMAL DESCRIPTION OF ALTRAN USING LINKED FOREST MANIPULATION SYSTEMS", Technical Report CS-73-08, University of
Waterloo, April, 1973.
1821:
98:
rational algebra package, and “can be thought of as a variant of FORTRAN with the addition of an extra declaration, the ‘algebraic’ type declaration.”
1258:
2103:
108:
ALTRAN should not be confused with the ALGOL to FORTRAN Translator, called Altran, that "converts
Extended Algol programs into Fortran IV."
2108:
1793:
A.D. Hall and S.C. Johnson, "ALTRAN programs for SIGSAM problem #6", ACM SIGSAM Bulletin, Volume 8 Issue 2, May 1974, p. 12 - 36.
1376:
148:, which was highly portable. The translator was implemented by Ritchie, the interpreter by Hall, the run-time rational function and
1758:
1814:
1539:
766:
1790:
Stuart I. Feldman, "A brief description of Altran", ACM SIGSAM Bulletin, Volume 9 Issue 4, November 1975, p. 12 - 20.
1871:
2113:
2069:
1807:
1670:
1607:
1573:
2081:
2020:
1906:
1861:
183:
1697:
1959:
1846:
679:
102:
1698:"Computing Science Technical Report No. 99 – A History of Computing Research at Bell Laboratories (1937–1975)"
1876:
131:
and W. Stanley Brown in the middle 1960s. However, soon after the completion of their ALTRAN translator, the
595:
171:
1999:
1631:
1851:
1511:
889:
525:
455:
2015:
160:
1830:
1728:
1529:
1660:
1597:
19:
This article is about the FORTRAN extension. For Altran
Technologies, a consulting firm, see
1563:
1941:
1838:
83:
8:
1974:
1916:
1747:
1949:
1787:
W.S. Brown, ALTRAN User's Manual (3rd ed.), Bell
Laboratories, Murray Hill, N.J., 1973.
1784:
W.S. Brown, ALTRAN User's Manual (2nd ed.), Bell
Laboratories, Murray Hill, N.J., 1972.
137:
42:
1891:
1666:
1603:
1569:
1535:
121:
87:
1964:
1994:
1954:
128:
32:
1509:
Hall, A.D., "The ALTRAN System for
Rational Function Manipulation — A Survey".
145:
141:
1355:{\displaystyle {\frac {\partial }{\partial y}}(2x+5xy^{2}-3y^{3})=10xy-9y^{2}}
2097:
1705:
1989:
1799:
152:
routines by
Feldman, Hall, and Johnson, and the I/O routines by Johnson.
2040:
149:
117:
409:# WE HAVE WRITTEN A SIMPLE PROGRAM ON UNIT 25, NOW WE INVOKE FTNOUT TO
1886:
1701:
167:
124:. These subroutines were themselves rewritten in FORTRAN for ALTRAN.
91:
47:
90:
of several variables with integer coefficients. It was developed at
2030:
1911:
1896:
163:
132:
2035:
1969:
1901:
67:
2045:
2025:
1983:
1866:
1473:{\displaystyle \mathrm {GCD} (x^{2}-y^{2},x^{2}+2xy+y^{2})=x+y}
175:
20:
1979:
1931:
1921:
1881:
1856:
1562:
Geddes, Keith O.; Czapor, Stephen R.; Labahn, George (2007).
95:
1726:
1926:
1230:
179:
71:
116:
ALPAK, written in 1964, originally consisted of a set of
174:. They found that "ALTRAN is about 15 times faster than
1534:. Springer Science & Business Media. p. 364.
1379:
1261:
883:
859:{\displaystyle (x+y)^{3}=x^{3}+3x^{2}y+3xy^{2}+y^{3}}
769:
682:
598:
528:
458:
182:
environment, and it is at least 12 times faster than
1568:. Springer Science & Business Media. p. 4.
1561:
1472:
1354:
1236:
858:
744:
657:
573:
503:
2095:
1527:
385:"C EXAMPLE PROG WRITTEN WITH FTNOUT."
1815:
1829:
127:An early version of ALTRAN was developed by
745:{\displaystyle (x^{2}-y^{2})\div (x+y)=x-y}
16:Variant of the FORTRAN programming language
2076:
1822:
1808:
1602:. Cambridge University Press. p. 21.
1696:Holbrook, Bernard D.; Brown, W. Stanley.
1695:
1662:Computer Algebra: Concepts and Techniques
1523:
1521:
94:in 1960s. ALTRAN is a FORTRAN version of
1745:
1691:
1689:
1505:
1503:
1501:
1499:
1497:
1495:
1727:Johnson, S. C.; Ritchie, D. M. (1976).
1658:
2104:Computer-related introductions in 1968
2096:
1764:from the original on September 3, 2019
1739:
1531:Recent Advances in Dynamical Astronomy
1528:Tapley, B.D.; Szebehely, V.G. (2012).
1518:
658:{\displaystyle (x+y)(x-y)=x^{2}-y^{2}}
412:# THIS ALTRAN OUTPUT TO LEGAL FORTRAN.
1803:
1686:
1595:
1492:
2109:Fortran programming language family
13:
1629:
1387:
1384:
1381:
1268:
1264:
159:In 1979, ALTRAN was ported to the
14:
2125:
189:
2075:
2064:
2063:
429:Elementary operations in ALTRAN
1748:"AFWL Implementation of ALTRAN"
1565:Algorithms for Computer Algebra
86:for the formal manipulation of
1720:
1652:
1623:
1589:
1555:
1515:, 14(8):517–521 (August 1971).
1455:
1391:
1321:
1277:
1171:
1145:
1106:
1094:
1091:
1079:
1047:
1029:
917:
899:
783:
770:
727:
715:
709:
683:
626:
614:
611:
599:
574:{\displaystyle (x+y)-(x-y)=2y}
559:
547:
541:
529:
504:{\displaystyle (x+y)+(x-y)=2x}
489:
477:
471:
459:
1:
1632:"ALGOL TO FORTRAN TRANSLATOR"
1485:
423:
382:" FUNCTION F(X,Y)"
172:Air Force Weapons Laboratory
82:(ALgebraic TRANslator) is a
7:
2000:Engineering Equation Solver
1659:Lamagna, Edmund A. (2019).
48:Bell Telephone Laboratories
10:
2130:
111:
18:
2059:
2008:
1940:
1837:
1665:. CRC Press. p. 12.
1596:Brown, P.J., ed. (1977).
1512:Communications of the ACM
66:
61:
53:
41:
31:
2114:Computer algebra systems
1831:Computer algebra systems
1366:Greatest Common Divisor
756:Integral exponentiation
193:
161:Control Data Corporation
1746:Rhoades, Jr., Cecil E.
440:Example on polynomials
120:for FORTRAN written in
1986:symbolic math toolbox)
1474:
1356:
1238:
860:
746:
659:
575:
505:
1475:
1357:
1239:
861:
747:
660:
576:
506:
1708:on September 2, 2014
1599:Software Portability
1377:
1259:
881:
767:
680:
596:
526:
456:
84:programming language
874:G = F(X = P, Y = Q)
430:
397:" RETURN"
54:First appeared
28:
1729:"Unix Portability"
1470:
1352:
1234:
1229:
1225:
856:
742:
655:
571:
501:
428:
138:Stephen C. Johnson
129:M. Douglas McIlroy
88:rational functions
26:
2091:
2090:
1639:slac.stanford.edu
1630:Wilner, Wayne T.
1541:978-94-010-2611-6
1483:
1482:
1275:
170:computers at the
146:Stuart I. Feldman
142:Dennis M. Ritchie
122:assembly language
77:
76:
2121:
2079:
2078:
2067:
2066:
1950:ClassPad Manager
1824:
1817:
1810:
1801:
1800:
1774:
1773:
1771:
1769:
1763:
1752:
1743:
1737:
1736:
1724:
1718:
1717:
1715:
1713:
1704:. Archived from
1693:
1684:
1683:
1681:
1679:
1656:
1650:
1649:
1647:
1645:
1636:
1627:
1621:
1620:
1618:
1616:
1593:
1587:
1586:
1584:
1582:
1559:
1553:
1552:
1550:
1548:
1525:
1516:
1507:
1479:
1477:
1476:
1471:
1454:
1453:
1429:
1428:
1416:
1415:
1403:
1402:
1390:
1371:
1361:
1359:
1358:
1353:
1351:
1350:
1320:
1319:
1304:
1303:
1276:
1274:
1263:
1253:
1248:Differentiation
1243:
1241:
1240:
1235:
1233:
1232:
1226:
1222:
1221:
1203:
1199:
1198:
1186:
1185:
1170:
1169:
1157:
1156:
1138:
1134:
1133:
1121:
1120:
1072:
1021:
1020:
1008:
1007:
875:
865:
863:
862:
857:
855:
854:
842:
841:
820:
819:
804:
803:
791:
790:
761:
751:
749:
748:
743:
708:
707:
695:
694:
674:
664:
662:
661:
656:
654:
653:
641:
640:
590:
580:
578:
577:
572:
520:
510:
508:
507:
502:
450:
431:
427:
419:
416:
413:
410:
407:
406:" END"
404:
401:
398:
395:
392:
389:
386:
383:
380:
377:
374:
371:
368:
365:
362:
359:
356:
353:
350:
347:
344:
341:
338:
335:
332:
329:
326:
323:
320:
317:
314:
311:
308:
305:
302:
299:
296:
293:
290:
287:
284:
281:
278:
275:
272:
269:
266:
263:
260:
257:
254:
251:
248:
245:
242:
239:
236:
233:
230:
227:
224:
221:
218:
215:
212:
209:
206:
203:
200:
197:
37:W. Stanley Brown
33:Designed by
29:
25:
2129:
2128:
2124:
2123:
2122:
2120:
2119:
2118:
2094:
2093:
2092:
2087:
2055:
2004:
1995:TI InterActive!
1936:
1833:
1828:
1778:
1777:
1767:
1765:
1761:
1750:
1744:
1740:
1725:
1721:
1711:
1709:
1694:
1687:
1677:
1675:
1673:
1657:
1653:
1643:
1641:
1634:
1628:
1624:
1614:
1612:
1610:
1594:
1590:
1580:
1578:
1576:
1560:
1556:
1546:
1544:
1542:
1526:
1519:
1508:
1493:
1488:
1449:
1445:
1424:
1420:
1411:
1407:
1398:
1394:
1380:
1378:
1375:
1374:
1369:
1346:
1342:
1315:
1311:
1299:
1295:
1267:
1262:
1260:
1257:
1256:
1251:
1228:
1227:
1224:
1223:
1217:
1213:
1201:
1200:
1194:
1190:
1181:
1177:
1165:
1161:
1152:
1148:
1136:
1135:
1129:
1125:
1116:
1112:
1070:
1069:
1050:
1023:
1022:
1016:
1012:
1003:
999:
992:
986:
985:
969:
963:
962:
946:
940:
939:
920:
892:
885:
884:
882:
879:
878:
873:
850:
846:
837:
833:
815:
811:
799:
795:
786:
782:
768:
765:
764:
759:
703:
699:
690:
686:
681:
678:
677:
672:
649:
645:
636:
632:
597:
594:
593:
588:
585:Multiplication
527:
524:
523:
518:
457:
454:
453:
448:
426:
421:
420:
417:
414:
411:
408:
405:
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312:
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288:
285:
282:
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261:
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228:
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219:
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210:
207:
204:
201:
198:
195:
192:
114:
103:macro processor
24:
17:
12:
11:
5:
2127:
2117:
2116:
2111:
2106:
2089:
2088:
2086:
2085:
2073:
2060:
2057:
2056:
2054:
2053:
2048:
2043:
2038:
2033:
2028:
2023:
2018:
2012:
2010:
2006:
2005:
2003:
2002:
1997:
1992:
1987:
1977:
1972:
1967:
1962:
1957:
1952:
1946:
1944:
1938:
1937:
1935:
1934:
1929:
1924:
1919:
1914:
1909:
1904:
1899:
1894:
1889:
1884:
1879:
1874:
1869:
1864:
1859:
1854:
1849:
1843:
1841:
1835:
1834:
1827:
1826:
1819:
1812:
1804:
1798:
1797:
1794:
1791:
1788:
1785:
1782:
1776:
1775:
1738:
1719:
1685:
1671:
1651:
1622:
1608:
1588:
1574:
1554:
1540:
1517:
1490:
1489:
1487:
1484:
1481:
1480:
1469:
1466:
1463:
1460:
1457:
1452:
1448:
1444:
1441:
1438:
1435:
1432:
1427:
1423:
1419:
1414:
1410:
1406:
1401:
1397:
1393:
1389:
1386:
1383:
1372:
1367:
1363:
1362:
1349:
1345:
1341:
1338:
1335:
1332:
1329:
1326:
1323:
1318:
1314:
1310:
1307:
1302:
1298:
1294:
1291:
1288:
1285:
1282:
1279:
1273:
1270:
1266:
1254:
1252:G = DIFF(F, Y)
1249:
1245:
1244:
1231:
1220:
1216:
1212:
1209:
1206:
1204:
1202:
1197:
1193:
1189:
1184:
1180:
1176:
1173:
1168:
1164:
1160:
1155:
1151:
1147:
1144:
1141:
1139:
1137:
1132:
1128:
1124:
1119:
1115:
1111:
1108:
1105:
1102:
1099:
1096:
1093:
1090:
1087:
1084:
1081:
1078:
1075:
1073:
1071:
1068:
1065:
1062:
1059:
1056:
1053:
1051:
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1046:
1043:
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1037:
1034:
1031:
1028:
1025:
1024:
1019:
1015:
1011:
1006:
1002:
998:
995:
993:
991:
988:
987:
984:
981:
978:
975:
972:
970:
968:
965:
964:
961:
958:
955:
952:
949:
947:
945:
942:
941:
938:
935:
932:
929:
926:
923:
921:
919:
916:
913:
910:
907:
904:
901:
898:
895:
894:
891:
890:
888:
876:
871:
867:
866:
853:
849:
845:
840:
836:
832:
829:
826:
823:
818:
814:
810:
807:
802:
798:
794:
789:
785:
781:
778:
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772:
762:
757:
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741:
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732:
729:
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723:
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631:
628:
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619:
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610:
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591:
586:
582:
581:
570:
567:
564:
561:
558:
555:
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543:
540:
537:
534:
531:
521:
516:
512:
511:
500:
497:
494:
491:
488:
485:
482:
479:
476:
473:
470:
467:
464:
461:
451:
446:
442:
441:
438:
437:ALTRAN syntax
435:
425:
422:
194:
191:
190:Sample program
188:
113:
110:
75:
74:
64:
63:
59:
58:
55:
51:
50:
45:
39:
38:
35:
15:
9:
6:
4:
3:
2:
2126:
2115:
2112:
2110:
2107:
2105:
2102:
2101:
2099:
2084:
2083:
2074:
2072:
2071:
2062:
2061:
2058:
2052:
2049:
2047:
2044:
2042:
2039:
2037:
2034:
2032:
2029:
2027:
2024:
2022:
2019:
2017:
2014:
2013:
2011:
2007:
2001:
1998:
1996:
1993:
1991:
1988:
1985:
1981:
1978:
1976:
1973:
1971:
1968:
1966:
1963:
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1756:
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1723:
1707:
1703:
1699:
1692:
1690:
1674:
1672:9781138093140
1668:
1664:
1663:
1655:
1640:
1633:
1626:
1611:
1609:0-521-29725-7
1605:
1601:
1600:
1592:
1577:
1575:0-7923-9259-0
1571:
1567:
1566:
1558:
1543:
1537:
1533:
1532:
1524:
1522:
1514:
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1500:
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1436:
1433:
1430:
1425:
1421:
1417:
1412:
1408:
1404:
1399:
1395:
1373:
1370:D = GCD(A, B)
1368:
1365:
1364:
1347:
1343:
1339:
1336:
1333:
1330:
1327:
1324:
1316:
1312:
1308:
1305:
1300:
1296:
1292:
1289:
1286:
1283:
1280:
1271:
1255:
1250:
1247:
1246:
1218:
1214:
1210:
1207:
1205:
1195:
1191:
1187:
1182:
1178:
1174:
1166:
1162:
1158:
1153:
1149:
1142:
1140:
1130:
1126:
1122:
1117:
1113:
1109:
1103:
1100:
1097:
1088:
1085:
1082:
1076:
1074:
1066:
1063:
1060:
1057:
1054:
1052:
1044:
1041:
1038:
1035:
1032:
1026:
1017:
1013:
1009:
1004:
1000:
996:
994:
989:
982:
979:
976:
973:
971:
966:
959:
956:
953:
950:
948:
943:
936:
933:
930:
927:
924:
922:
914:
911:
908:
905:
902:
896:
886:
877:
872:
870:Substitution
869:
868:
851:
847:
843:
838:
834:
830:
827:
824:
821:
816:
812:
808:
805:
800:
796:
792:
787:
779:
776:
773:
763:
758:
755:
754:
739:
736:
733:
730:
724:
721:
718:
712:
704:
700:
696:
691:
687:
676:
671:
668:
667:
650:
646:
642:
637:
633:
629:
623:
620:
617:
608:
605:
602:
592:
587:
584:
583:
568:
565:
562:
556:
553:
550:
544:
538:
535:
532:
522:
517:
514:
513:
498:
495:
492:
486:
483:
480:
474:
468:
465:
462:
452:
447:
444:
443:
439:
436:
433:
432:
187:
185:
181:
177:
173:
169:
165:
162:
157:
153:
151:
147:
143:
139:
134:
130:
125:
123:
119:
109:
106:
104:
99:
97:
93:
89:
85:
81:
73:
69:
65:
62:Influenced by
60:
56:
52:
49:
46:
44:
40:
36:
34:
30:
22:
2080:
2068:
2050:
2009:Discontinued
1990:SMath Studio
1766:. Retrieved
1754:
1741:
1732:
1722:
1710:. Retrieved
1706:the original
1676:. Retrieved
1661:
1654:
1642:. Retrieved
1638:
1625:
1613:. Retrieved
1598:
1591:
1579:. Retrieved
1564:
1557:
1545:. Retrieved
1530:
1510:
515:Subtraction
158:
154:
126:
115:
107:
100:
79:
78:
1975:Mathematica
1942:Proprietary
1839:Open-source
1712:February 2,
118:subroutines
105:called M6.
2098:Categories
2041:Mathomatic
1486:References
434:Operation
424:Operations
196:PROCEDURE
150:polynomial
1927:Xcas/Giac
1887:Macaulay2
1702:Bell Labs
1405:−
1337:−
1306:−
1269:∂
1265:∂
1159:−
1101:−
980:−
737:−
713:÷
697:−
669:Division
643:−
621:−
554:−
545:−
484:−
445:Addition
226:ALGEBRAIC
168:Cyber 176
92:Bell Labs
43:Developer
2070:Category
2031:LiveMath
1917:Singular
1912:SageMath
1897:Normaliz
1759:Archived
1755:dtic.mil
760:D = A**K
289:REQUIRES
133:IBM 7094
2036:Macsyma
1970:Mathcad
1902:PARI/GP
1852:Cadabra
1734:itself.
673:D = A/B
589:C = A*B
519:C = A-B
449:C = A+B
340:1000000
208:EXAMPLE
112:History
68:FORTRAN
2051:ALTRAN
2046:muMATH
2026:Erable
2021:Derive
1984:MATLAB
1907:Reduce
1892:Maxima
1867:FriCAS
1862:Fermat
1768:Sep 3,
1678:Sep 3,
1669:
1644:Sep 3,
1615:Sep 3,
1606:
1581:Sep 3,
1572:
1547:Sep 3,
1538:
415:FTNOUT
364:PRINT
355:WRITE
313:EXPAND
298:LENGTH
286:FTNOUT
262:FTNOUT
259:ALTRAN
220:FTNOUT
205:SIMPLE
184:REDUCE
176:FORMAC
144:, and
80:ALTRAN
27:ALTRAN
21:Altran
2016:CAMAL
1980:muPAD
1965:Maple
1960:Magma
1932:Yacas
1922:SymPy
1882:GiNaC
1857:CoCoA
1847:Axiom
1762:(PDF)
1751:(PDF)
1635:(PDF)
370:WRITE
223:LONG
178:in a
96:ALPAK
2082:List
1955:KANT
1872:FORM
1770:2019
1714:2020
1680:2019
1667:ISBN
1646:2019
1617:2019
1604:ISBN
1583:2019
1570:ISBN
1549:2019
1536:ISBN
295:LINE
265:OPTS
214:USE
199:MAIN
180:PL/I
166:and
164:6600
72:PL/I
57:1965
1877:GAP
418:END
271:201
2100::
1757:.
1753:.
1731:.
1700:.
1688:^
1637:.
1520:^
1494:^
1328:10
376:25
346:**
304:72
301:OF
277:72
250:10
238:10
217:OF
211:OF
140:,
70:,
1982:(
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1809:v
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1716:.
1682:.
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1468:y
1465:+
1462:x
1459:=
1456:)
1451:2
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1440:y
1437:x
1434:2
1431:+
1426:2
1422:x
1418:,
1413:2
1409:y
1400:2
1396:x
1392:(
1388:D
1385:C
1382:G
1348:2
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1340:9
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1322:)
1317:3
1313:y
1309:3
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1297:y
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1272:y
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1208:=
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1080:(
1077:=
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1033:p
1030:(
1027:f
1018:2
1014:y
1010:+
1005:2
1001:x
997:=
990:r
983:y
977:x
974:=
967:q
960:y
957:+
954:x
951:=
944:p
937:z
934:+
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928:x
925:=
918:)
915:z
912:,
909:y
906:,
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900:(
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806:+
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793:=
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780:y
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771:(
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725:y
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367:F
361:#
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328:2
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319:(
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310:=
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283:#
280:)
274:,
268:(
256:F
253:)
247::
244:Y
241:,
235::
232:X
229:(
202:#
23:.
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