Richard Pavelle (auth.), Richard Pavelle (eds.)'s Applications of Computer Algebra PDF

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

ISBN-10: 146846888X

ISBN-13: 9781468468885

ISBN-10: 1468468901

ISBN-13: 9781468468908

Today, convinced software program platforms exist which surpass the computational skill of researchers while their mathematical thoughts are utilized to many components of technological know-how and engineering. those computers can practice a wide component to the calculations visible in mathematical research. regardless of this huge strength, hundreds of thousands of individuals use those structures as a regimen source for daily calculations. those software program courses are typically known as "Computer Algebra" platforms. they've got names reminiscent of MACSYMA, MAPLE, muMATH, decrease and SMP. they're receiving credits as a computational relief with in­ creasing regularity in articles within the clinical and engineering literature. while most folk take into consideration pcs and clinical learn nowadays, they think a desktop grinding away, processing numbers arithmetically. it's not in most cases discovered that, for a few years, desktops were acting non-numeric computations. this implies, for instance, that one inputs an equa­ tion and obtains a closed shape analytic resolution. it truly is those laptop Algebra platforms, their functions, and functions that are the topic of the papers during this volume.

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It is complicated by the exponent 4 in the integrand. Numeric methods would not suffice in this case because of the two parameters in the integrand. We gave him an account to use MACSYMA on the MIT-MC machine, he typed in the expression, and 10 seconds later had the answer. If you count the terms, after expanding out (D2), you will fmd 70. This explains why it is so tricky to correctly evaluate the integral by hand. INTEGRATE; Time= 10488 msec. 3 4 2 (02) N (K LOG(N) - 2 N + 3 N + B) 3 2 3 2 + 2 N (3 N - 4 N - 2 K) (K LOG(N) - 2 N + 3 N + B) + N (1080 N - 2940 N 6 5 + 3 4 2016 N - 1575 K N + 3 2 2240 K N 2 + 840 K ) 3 2 2 (K LOG(N) - 2 N + 3 N + B) 170 + 9 8 7 6 6 N (272160 N - 1125600 N + 1561140 N - 631800 K N - 725760 N + 5 4 2 3 2 2 1808100 K N - 1298304 K N + 694575 K N - 1019200 K N 3 3 2 - 352800 K ) (K LOG(N) - 2 N + 3 N + B)/14700 42 3 4 9 2 N (42768 N - 237952 N + 498966 N - 467181 N + 164736) + --------------------------------------------------------- 5005 7 3 2 K N (2437776 N - 10510000 N + 15149673 N - 7299072) 88200 2 5 2 K N (23996250 N - 70529375 N + 51894528) + ----------~-------------------------------- 514500 3 3 5 K N (1377 N - 2048) 4 - ----------------------- + 24 K N 144 Actually, the researcher needed the FORTRAN expression for the integral in (02).

This is shown in (C4). 28 (C4) G:F+L1*K1+LZ*K2; Z (D4) G = Z + Z + Zv v+ LZ (Z - Z + 2 x + T 2 X+ Z T + B) + Ll (- Z + 3 V+ X+ T + A) The next step is to form all partial derivatives of G as shown in (CS). (C5) [DIFF(G,X),DIFF(G,V),DIFF(G,Z),DIFF(G,T),DIFF(G,LI),DIFF(G,L2)]; (D5) [2 X + Z LZ 2 T + 2 LZ Ll, 4 V - L2 + + + 3 Ll, 2 Z L1, - Z + 3 V + X + T + + L2 - Ll, A, Z - v+ 2 X+ Z T + B] We then solve the system (D5) for each of the six parameters. (C6) SOLVE(D5,[X,V,Z,T,Ll,L2]); 27 B (D6) [[X 13 A 23 B + 13 A = - ----------- Z 19 A - 3 8 Ll 138 11 A - 9 B 5 A - 2 B 138 27 T + = - -----------, v = - --------- = ---------69 = ---------69 A - 5 B L2 = - -------]] 23 For the final step we substitute (D6) into F as defined in (01).

The solution (D6) is given in terms of rational numbers, exactly. Notice the near mathematical syntax in the MACSYMA commands. To use MACSYMA, one communicates in a kind of mathematical language rather than a strict programming language. E); Time- 1355 msec. (06) [ 10922 V - 14259 X + 2706 S + 1207 R A,. - ----------------------------------284 64008 V - 64505 X - 14271 T + 7667 S + 10863 R B = ---------------------------------------------852 C =- 8128 V - 4365 X - 4757 T - 1845 S + 3621 R -----------------------------------------284 3048 V - 776 X - 4757 T + 2583 S o • - -------------------------------284 3810 V + 5917 X - 14271 T + 2501 S + 3621 R E • ------------------------------------------852 MACSYMA can also deal with systems of non-linear algebraic equations.

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Applications of Computer Algebra by Richard Pavelle (auth.), Richard Pavelle (eds.)


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