Computer algebra is a diffuse branch of mathematics done with computers that encompasses
both computational algebra and analysis.
Computer algebra includes exact symbolic manipulation of mathematical expressions, such as polynomialcomputation,
symbolic integration, symbolic summation,
and equation solving. Practical symbolic
integration systems combine decision procedures such as the Risch
algorithm with heuristic, table-based, and rule-based methods; even when an elementary
antiderivative exists, implementations may miss
it (Desmond 2026).
Computer algebra can also supply exact checks for results proposed in AI-assisted mathematics. For example, a claimed antiderivative
can be tested by differentiation and simplification
to determine whether it reproduces the integrand. Such
a check verifies the resulting identity, not the correctness
or significance of the process that produced the candidate (Wolfram 2026).
Formal proof checking additionally verifies the inference steps and assumptions of a complete derivation. Symbolic calculation can support
such an argument, but simplifying an expression or testing a numerical example does
not check the complete derivation.
