CALTRAN(ID:4405/cal013)

CALTECH Algebra package 

for CALTECH TRANslator

Package of FORTRAN algebraic subroutines
References:
  • Kitselman, A.L. "CALPAK and CALTRAN" La Jolla, Calif., 1965. (Unpublished, cited in Sammet (1966)) view details
  • Ketselman review of Tobey 1965 (FORMAC) view details Extract: CALTRAN
    Another language in this same field, CALTRAN, tackles this same problem of "intermediate swell" in forming a product by using Pacioli multiplication (which stores no intermediate products) and positional representation of monomials [ for example, 7 3 stored in A (4,5,G) means that expression A contains the monomial 73.345 ] Extract: FORMAC
    In this article, one of the architects of FORMAC presents
    an interesting discussion of the problems encountered in obtaining the product of two polynomials, differentiating polynomial, and organizing the resulting expressions. The FORMAC operations used are EXPAND, AUTSIM, LEXICO, FMCDIF, FMCSEX, and SHRINK.

    If raised to the sixth power, hundreds of intermediate products are involved, although the final expression contains only 31 terms. In FORMAC, which is designed to handle and express each monomial in full, this expanding and condensing requires much storage; so much thought has been given to finding algorithms which permit economy. This is a formidable problem in the important and growing field of what is coming to be called "big math."

    [...]

    It seems to this reviewer that FORMAC output expressions are awkward to read; how about a code for writing them on a plotter?
          in ACM Computing Reviews 7(06) November-December 1966 view details
  • Sammet, Jean E. "Survey of formula manipulation" view details
          in [ACM] CACM 9(08) August 1966 view details