Polynomial Factoring.
Tensors.
Most of JACAL
The maintainer can be reached as ‘agj@alum.mit.edu’.
In December of 1987, in order to facilitate the design of constant impedance electrical filters (diplexers), I (Aubrey Jaffer) wrote a symbolic circuit analysis program. It was written in LISP and implemented canonical rational expressions. It worked directly with the small signal Laplace Transform of currents, voltages, and impedances. After doing some reading about symbolic manipulation, I became fascinated with the problem of canonical forms. That interest produced JACAL, an interactive symbolic mathematics program similar to Maxima.
The canonical aspect of JACAL is that all equations and expressions undergo nomalization such that two formulas which are equivalent have the same representation. Note that formulas with different variable orderings will not appear the same.
JACAL provides some functions which it does not canonicalize:
imagpart, realpart, abs, and cabs.
Fractional roots are not guaranteed to be positive, but they are
linked; thus sqrt(a+z)-sqrt(a+z) ⇒ 0. Also, roots of
-1 cannot be canonicalized.
I initially used JACAL for electronics modeling, handling equations complicated enough that error-free pencil and paper manipulations were difficult. As JACAL’s capabilities grew, more applications were found.
Around 1993-1995 Mike Thomas added univariate and multivariate polynomial factorization. In 1993-1997, Jerry D. Hedden added tensor manipulations to JACAL.
Having retired, in 2024 I finally implemented indefinite integration (actually anti-differentiation) of rational functions incorporating radicals.
Spurred by my mathematical physics work in fluid-mechanics, I
implemented logarithms, exponentials, Lambert-W (the inverse of
x*exp(x)), and trigonometric functions as the solutions to
ordinary differential equations (ODE).
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