Symbolic Script Programming for Java

Computer algebra in Java is a promising field of development. It has not yet reached an industrial strength, in part because of a lack of good user interfaces. Using a general purpose scripting language can bring a natural mathematical notation, akin to the one of specialized interfaces included in most computer algebra systems. We present such an interface for Java computer algebra libraries, using scripts available in the JSR 223 framework. We introduce the concept of `symbolic programming’ and show its usefulness by prototypes of symbolic polynomials and polynomial rings.

💡 Research Summary

The paper addresses the longstanding usability gap in Java‑based computer algebra systems (CAS). While Java offers strong performance and a clean object‑oriented design, existing CAS libraries lack a natural, mathematically‑oriented user interface, limiting their adoption in industrial settings. To bridge this gap, the authors propose using general‑purpose scripting languages that conform to the JSR‑223 “Scripting for the Java Platform” framework as a front‑end for Java algebra libraries.

A central contribution is the introduction of “symbolic programming,” a meta‑programming technique that treats an expression as reconstructing when its textual representation (e.g., the result of toString() in Java) is itself a valid expression in the same language. The paper formalizes this notion through a series of definitions: a reconstructing expression must be syntactically valid and have identical input and output forms; a context is a set of variable and function definitions that makes reconstruction possible; a symbolic object is any object whose output form is reconstructing within a given context; a symbolic type is a type whose every instance can be made symbolic in some context; and a symbolic container type is a collection whose elements are all symbolic.

Using these definitions, the authors analyze common Java and Scala types. Primitive int is symbolic because 1 prints as 1, whereas String is not because "hello".toString() yields hello without quotes. Scala’s `List