My two cents:
“Scientist’s CAS” mainly focuses algebraic computation and manipulation of variables/arrays/matrixes in the real number or complex number field.
In other words, we need a framework where normal computational code can be analyzed and transformed symbolically without extra work (the fusion of symbolic code and numerical code). It is more like a symbolic plugin to aid numerical scientific computation.
By contrast, “mathematician’s CAS” pays more attention to mathematical structures and catogories, such as number theory and group theory.
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