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By Karakhanyan M.I., Khor'kova T.A.

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Hundreds of CPU hours were saved in a particu1ar research project. Below are equivalent expressions (setting constants to unity) for the Planck integral in the wavelength and frequency domains. 3 I I [ [ V ] V I -------------- dl • I ------- dV ] 5 III I l CXE - 1) I XE - 1 We next rewrite the integrand as a powerseries. INF 3 V ------- = XE V -1 3 - V V XE 3 V XE ------ .. _- v \ I - V 1 - XE > INF IE - NV 3 \ =V I N=O > XE -NV N=l We now integrate the last term on the right above, with respect to V, to find the known powerseries expansion for the Planck integral.

1 Component Tensor Manipulation The Component Tensor Manipulation Program, CTENSR, provides the user with tools for computing many of the geometrical objects encountered in General Relativity and Differential Geometry. For a given metric tensor, CTENSR can compute the Christoffel gymbols, the curvature tensor, the Weyl tensor, the Einstein and Ricci tensors, the geodesic equations of motion, and other useful geometrical objects. In the example below, CTENSR is used to reproduce Dingle's formulas [Dill.

35 6. Applications of MACSYMA Over the last 10 years I have used MACSYMA on a 1arge number of problems submitted by researchers who have not had access to Computer Algebra systems. I have chosen a few of these problems to illustrate the power and utility of MACSYMA. These examples should give the reader some ideas for adapting the system to meet their own needs. Unfortunately, many of these problems were sent without any indication to the user's motivation fo; studying them. Users often tend to shy away from describing the significance of their problems, especially when the problems have commercial or military implications.

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