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Extra info for Euler equations on nonsolvable Lie Algebras with nontrivial radical
As CAS become official accessories to a course their use needs to be institutionalized, usually by incorporating a computer-lab as a compulsory component of a course. While, on one level, this might be thought of simply as an organizational aspect, most often the computer-lab is associated with a shift in the type of mathematical activities to one involving guided investigations, generation of exemplars, hypotheses and counter-examples. For example, a CAS-lab may be devoted to investigating the difference quotient (f(x+h)-f(x»/h of a function f.
As of 1980, most of the sixty-some existing computer algebra systems were special-purpose systems designed to solve specific problems either in mathematical physics (general relatively, quantum mechanics) and theoretical chemistry. ". It is worth noting that they said little about the computer algebra in relation to mathematics most systems in those days were conceived primarily as tools for solving problems in science. One exception was ALTRAN, a computer algebra programme for solving polynomial and rational functions.
The analytical solution for f =0 produces three different-looking (and difficult-toread) values ("1" is MAPLE's notation for sqrt(-l». When the three solutions are collected into a list and then evaluated over the complex field using evalc, it becomes apparent that there is but a single solution repeated three times. 5:=["]; • evalc(5); 2 2, (- 1/2 21/3 + 1/2 31/2 21/3 I) 3 , (- 1/2 21/3 - 1/2 31/2 2 1/3 I) 3 2 , ( - 1/2 21/3 + 1/2 31/2 21/3 I) 3 , (- 1/2 21/3 - 1/2 31/2 21/3 I) 3 ] [2, 2, 2] There are also difficulties with outputs to plotting routines - these will be discussed a bit further in the text.