Symbolic manipulation programs

Implementing the algorithm sketched above in the computer symbolic manipulation program FORM, as exemplified in Appendix A, and applying the method to the second-harmonic-generation (SHG) process, which is described by the interaction Hamiltonian Hi given by (55), one can easily calculate subsequent terms of the series (92). Restricting the calculations to the fourth-order terms, we get... 

The sign of the linear terms in (153) and (154) depends on the sign of Imp0, and this sign decides whether the quadrature is squeezed. These examples illustrate the effectiveness of the symbolic manipulation programs in obtaining such expansions. Previously such calculations have been performed by hand. This approach belongs to the standard methods of quantum optics, and many results based on the power series expansion have been discussed in the book [62], so we restrict ourselves to these few examples only. 

There are approximately 40 three loop diagrams to be computed for this reason the choice of the appropriate strategy is of significant importance. Any approach has to rely heavily on the use of symbolic manipulation computer programs. Our principal tool in this calculation is the so called integration-by-parts technique [9], which is common in perturbative calculations in high energy physics. 

All the above steps have been automated (in simple terms this means, that getting either the three loop g — 2 or the slope of the Dirac form factor is just a matter of changing a single line in the computer code). The program is written in Form, a symbolic manipulation language created by J.A.M. Vermaseren. Organization of the program is as follows ... 

A number of standard computer programs easily handle problems of this type such as spreadsheet packages, Matlab, Mathcad, Polymath, and so on as well as symbolic manipulators such as Mathematica, Maple, Derive, etc. Most statistic packages and equation solvers will also solve linear equations and have a simple user interface. 

Let us start with the short-time approximation in which we can use the symbolic manipulation computer program described in Appendix A to find the corrections coming from the quantum fluctuations of the fields. The operator formulas (94) and (95) are valid also for the degenerate downconversion because the two processes are governed by the same Hamiltonian, but now initially the second-harmonic mode is populated while the fundamental mode is initially in the vacuum state. Assuming that the pump mode at the frequency 2oo is in a coherent state fi0) (p0 = /Ni,exp(k )h)), we have... 

The present chapter will be mainly devoted to the three other approaches for structure determination, e. g. the Learning Machine Approach (LMA), the Deduction Programming Approach (DPA) and the Heuristic Programming Approach (HPA). Much emphasis will be put on the artificial intelligence approach where the computer is used as a symbol manipulator. The last section will introduce a new departure in the use of a computer for mass spectrometry, the area of theory formation and the proposal of fragmentation mechanisms. 

Using a symbolic manipulator for scalar arithmetic and an OOP-language for the rest. This is uncomfortable to program because of the two programming packages. 

Computers are well suited to the manipulation of numbers, but the ES relies on symbolic computation, in which symbols stand for properties, concepts, and relationships. The degree to which an ES can manage a task may depend on the complexity of the problem. For example, computer vision is an area of great interest within AI and many programs exist that can, without human assistance, use the output from a digital camera to extract information, such as the characters on a car number plate. However, automatic analysis of more complex images, such as a sample of soil viewed through a microscope, is far... 

Defining exactly which applications constitute AI is difficult in any field. The problem in chemistry is even worse because chemical applications that use AI methods often use numerical calculations. Some applications that are strictly numerical accomplish tasks similar to AI programs. The key feature used to limit the scope of this book was symbolic processing. The work presented includes expert systems, natural language applications, and manipulation of chemical structures. 

The systematic application of artificial intelhgence methods for the programmed manipulation of symbols in accordance with mathematical rules. Symbohc computing allows one to obtain symbolic solutions to equilibrium... 

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