This program is designed to operate on a system of equations, USA making user-specified substitutions and returning for each expression its partial derivatives with respect to a list of speci-Other computerson which operable: any IBM Series 360/370 fled variables. The output e,~pressionsfor the derivatives of computer, and any non-IBM computer with IBM 360/370-each input expression, in the form of statements directly compatible architecture usable in other programs, are organized into an array with subscripts corresponding to the variables by which it was dif-Operating system: MVS ferentiated. Output in eitherPL/1 [2], FORTRAN or SAS [3] syntax is available at user option. Programming language used: PL/1-FORMAC 73 [1] Method of~vlution High speed storage required: storage is dynamically allocated The program makes use of the powerful symbolic algebraic and released by the program as needed, depending on the manipulation facilities of the PL/1-FORMAC73 language. input data deck. The minimum available on the Penn. State system -300 Kbytesusually proves sufficient Restrictions on the complexityof the problem The maximum length of inpI~texpressions depends only on No. of bits in a word: 32 the limits inherent in the PL/1 compiler itself (32 765 characters (ref. [2], p. 4 11) in the current IBM implementation of Overlay structure: none required; however, the program con-PL/1). Output expressions are normally limited to 5000 charsists of a main program that calls three subroutines in succes-acters. There are no a priori Limits on the number of vansion, making feasible a simple overlay structure. This 15 ables, substitutions or expressions to be differentiated; these included along with the program deck are ultimately limited by installation resources and the No. of magnetic tapes required: none FORMAC system itself, and are unlikely to be exceeded by most users. The program can be used to determine derivatives Other peripherals used: card reader, line printer, card punch, beyond first order, up to a maximum of fourth order. disk Typical running time No. of cards in combined program and test deck: 1986 Approximately 22 CPU s are required for compilation and link-editing. Execution time of the resulting load module * Daniel W. Merdes was an employee of the Pennsylvania depends on the size and complexity of the data deck. A pre-State University Computation Center for a portion of the compiled and link-edited load module executed the test deck time that he worked on this program. shown in this paper in less than 1 CPU s.
00104655/81/0000-0000/s 02.75 Β© 1981 North-Holland * In place of the apostrophes ' 'used in this paper to delimit (2) Parameter list. These are the variables with a literal character string, for the computer input the apos-respect to which input expressions will be differentrophes' 'should be used. tiated. They are listed in order, each one surrounded *5*5* *5*5* IN "EO(2)", NOTiCE THAT TUE FUNCTION OPENATOLIS 'SIND' AND *5*5*