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Computer algebra and operators
The symbolic computation of operator expansions is discussed. Some of the capabilities that prove useful when performing computer algebra computations involving operators are considered. These capabilities may be broadly divided into three areas: the algebraic manipulation of expressions from the algebra generated by operators; the algebraic manipulation of the actions of the operators upon other mathematical objects; and the development of appropriate normal forms and simplification algorithms for operators and their actions. Brief descriptions are given of the computer algebra computations that arise when working with various operators and their actions
Can Computer Algebra be Liberated from its Algebraic Yoke ?
So far, the scope of computer algebra has been needlessly restricted to exact
algebraic methods. Its possible extension to approximate analytical methods is
discussed. The entangled roles of functional analysis and symbolic programming,
especially the functional and transformational paradigms, are put forward. In
the future, algebraic algorithms could constitute the core of extended symbolic
manipulation systems including primitives for symbolic approximations.Comment: 8 pages, 2-column presentation, 2 figure
Computational linear algebra over finite fields
We present here algorithms for efficient computation of linear algebra
problems over finite fields
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