By Richard Pavelle (auth.), Richard Pavelle (eds.)

Today, sure software program structures exist which surpass the computational skill of researchers while their mathematical thoughts are utilized to many components of technology and engineering. those computers can practice a wide element of the calculations obvious in mathematical research. regardless of this large strength, millions of individuals use those structures as a regimen source for daily calculations. those software program courses are in most cases referred to as "Computer Algebra" platforms. they've got names reminiscent of MACSYMA, MAPLE, muMATH, lessen and SMP. they're receiving credits as a computational relief with in creasing regularity in articles within the clinical and engineering literature. while most folks take into consideration desktops and clinical learn nowadays, they think a computing device grinding away, processing numbers arithmetically. it's not commonly discovered that, for a few years, pcs were acting non-numeric computations. this suggests, for instance, that one inputs an equa tion and obtains a closed shape analytic resolution. it really is those machine Algebra structures, their features, and functions that are the topic of the papers during this volume.

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To obtain the final form of the answer we factor (04). 0 msec. 2 2 2 C + B + A 2 5/2 312 2 2 2 P S (5 + P - 2 A ) XE (05) 5 2 + P - ------------------------------------------2 (5 2 7/2 + P ) The research program involves performing hundreds of integrations of this kind for different geometries. The integrands are similar to (01) and the computations equally complex. Although the answers look fairly simple when factored, the integration times are quite large. 4 Ouantum Theory/Gaining Insight Here is a problem in quantum theory that was proposed several years ago.

44 (01) [ 1, 117649 4782969 9 625 - 8 192 9216 81920 25937424601 23298085122481 88473600 14863564800 -------- ... -- --------------] (C2) FACTOR(Dl); 4 5 2 (02) 3 [ 1, 6 14 7 10 3 11 ---_ ... _- ... - 12 13 -----------] 10 2 14 3 6 17 3 2 20 4 2 2 2 3 2 3 2 5 2 3 5 2 3 5 7 From the form of the denominators in (D2) one gets the impression that factorials are present, and it is not difficult to guess at a possible form. Such a function is given below in (D3). 1 2 L - 2 (L - -) L 2 (03) F(L) := ---------------2 L!

2 Commodities Market/Cannot be Solved by Hand The following system of nonlinear equations occurred in a study of the commodities market. The person tried to solve the system by hand over a period of several months, and gave up. He tried numeric analysis and came to the incorrect conclusion that the system was singular. After suspending work on the equations for some time he contacted me to determine whether MACSYMA could help. The system of equations is shown in (D1). The variables are [S,T,U,V,W,x,y,Z).