Computer algebra

The complete vibration-rotation Flamiltonian for acetylene-like tetraatomic molecules has been derived by Handy et al. by hand [155] and using a computer algebra program [156]. (Note that in both of the mentioned papers there are some minor errors, see also [144,157,158]). Handy uses as bending coordinates... 

The analytical solution is rather tedious, but is aided by computer algebra software.)... 

Computer Algebra Capabilities and Applications to Problems in Engineering and the Sciences... 

My purpose in this paper is to provide a broad introduction to the capabilities of MACSYMA It is my hope that this information will create new users of Computer Algebra systems by showing what one might expect to gain by using them and what one will lose by not using them ... 

The user can explore extremely complex problems that cannot be solved in any other manner. This capability is often thought of as the major use of Computer Algebra systems. However, one should not lose sight of the fact that MACSYMA is often used as an advanced calculator to perform everyday symbolic and numeric problems. It also complements conventional tools such as reference tables or numeric processors. 

Uses It is difficult to list the application fields of MACSYMA because users often do not state the tools that helped them perform their research However, from Computer Algebra conferences ( 7,... 

Notice that KACSYKA has obtained the roots analytically and that numeric approximations have not been made. This demonstrates a fundamental difference between a Computer Algebra system and an ordinary numeric equation solver, namely the ability to obtain a solution without approximations. 1 could have given KACSYKA a "numeric" cubic equation in X by specifying numeric values for A and B. KACSYKA then would have solved the equation and given the numeric roots approximately or exactly depending upon the specified command. 

Pavelle, R. Rothstein, K. Fitch, J.P. Computer Algebra. Scientific American 1981, 245. 

Pavelle, R., Ed., "Applications of Computer Algebra" Rluwer Boston, 1985. 

R. Pavelle, ed. "Applications of Computer Algebra Kluwer Academic... 

The second section, on computer algebra, details chemical applications whose emphasis is on the mathematical nature of chemistry. As chemical theories become increasingly complex, the mathematical equations have become more difficult to apply. Symbolic processing simplifies the construction of mathematical descriptions of chemical phenomena and helps chemists apply numerical techniques to simulate chemical systems. Not only does computer algebra help with complex equations, but the techniques can also help students learn how to manipulate mathematical structures. 

Authors founded the kinetic polynomial theory in early 1980s (Lazman and Yablonskii, 1991 Lazman et ah, 1985a, 1985b, 1987a, 1987b Yablonskii et ah, 1982, 1983). It was further developed in collaboration with mathematicians Bykov and Kytmanov (Bykov et ah, 1987,1989). Later, applying computer algebra methods. 

Note that standard procedures, such as Groebner Bases, that are built into the modern computer algebra systems (e.g. Maple) cannot handle our systems efficiently (see monograph by Bykov et al., 1998). 

We have applied the computer algebra (Maple) to generate the partial sums corresponding to the "brackets" (55). 

Bykov, V. I., Kytmanov, A. M., and Lazman, M. Z., The modified elimination methods in computer algebra of polynomials. Abstracts of International Congress on Comp. Syst., and Appl. Math, pp. 106-107. St. Petersburg State Univ., St. Petersburg (1993). 

Lazman M., and Yablonsky G. Computer algebra in chemical kinetics Theory and application. Computer algebra in Scientific computing. Proceedings of CASC 2004, Muenchen, 313-324 (2004). 

The evaluation of fi2 follows the same recipe as that given above through the transformation to new variables x and y, the various partial derivatives d2gl/dx2 etc., and then to gl i. This manipulation requires patience or a computer algebra package (preferably both), but really we are only interested in the resulting expression which is... 

All computations used the GAP computer algebra system [GAP02] and the package PlanGraph ([Dut02]) by the second author the programs are available from [Du07]. 

Mag07] The MAGMA Group, Magma Computer Algebra System, Sydney University, 2007. 

In practice, the solution of polynomial equations is problematic if no simple roots are found by trial and error. In such circumstances the graphical method may be used or, in the cases of a quadratic or cubic equation, there exist algebraic formulae for determining the roots. Alternatively, computer algebra software (such as Maple or Mathematica, for example) can be used to solve such equations... 

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