Remark. from a presentation to checked representation data [fgap-001R]
AGENTDRAFTED
A finite presentation
\(\langle x_1,\ldots ,x_m\mid r_1,\ldots ,r_s\rangle \) gives a compact input
for algorithms that enumerate cosets, compute conjugacy classes, and build
character data. Sims develops the algorithms and the conditions under which
such computations terminate; Lux and Pahlings place them inside computational
representation theory.
The output has 3 possible evidential strengths. A transcript with
versioned inputs is reproducible. A compact certificate, such as matrices
satisfying the relations together with independently checked completeness
identities, can be verified without trusting the search. An unrecorded
software answer is neither. GAP is therefore a discovery and calculation
tool; its output becomes mathematics here only when the decisive relations
and completeness checks are visible. See
[sims1994computation, ch. 1] and
[lux2010representations, secs. 1.1 and 4.2].
The route is
\[
\begin {aligned}
\text {finite presentation}&\longrightarrow \text {computed candidates}\\
&\longrightarrow \text {checked relations and completeness}.
\end {aligned}
\]
The arrows distinguish generation from certification rather than describing
a project workflow.