# Identical Transformation

The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

## Identical Transformation

the replacement of one analytic expression by another that is equal to the first expression but is of different form. Identical transformations are used to put expressions in a form more convenient for carrying out numerical calculations, applying further transformations, taking logarithms, taking antilogarithms, differentiating, integrating, solving equations, and so on. Examples of identical transformations are multiplying out (removing parentheses), factoring, reducing algebraic fractions to a common denominator, decomposing algebraic fractions to sums of simple fractions, and reducing sums of trigonometric functions to a form suitable for taking logarithms (that is, transforming the sums into products).

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Model coordinates were then transformed to the local coordinate system applying identical transformation to the common reference points on the models and in the geodesic data.
Note that we keep an identical transformation in the regions x' < [x.sub.0] and x > [x.sub.0]+d, and therefore they are still free space after the transformation.
The slab region [x.sub.0] < x <[x.sub.0] + d (filled with the null-space medium) is compressed in the y direction and the other regions (free space regions) are still undergoing an identical transformation. In the compressed region [x.sub.0] < x < [x.sub.0] + d, the coordinate grid x = [x.sub.c] (parallel straight lines) is still transformed to x = [x.sub.c] and the coordinate grid y = [y.sub.c] is transformed to y' = f (x', [y.sub.c]) (compressed lines) whose slope dy'/dx' = df /dx determines the local direction of the transformed grid.
for pairwise different complex numbers [[lambda].sub.1], [[lambda].sub.2], ..., [[lambda].sub.m], where [epsilon] is the identical transformation and [theta] is the null transformation.
Note that people choose the identical transformation at the outer boundary of this kind of device, which is why such devices can only produce a local influence on electromagnetic waves.
We apply an identical transformation to the regions, excluding the region enclosed by [[GAMMA].sub.1] and [[GAMMA].sub.2].
At the input surface of our device, we have x' = x = 0, and thus y' = y and z' = z, which means an identical transformation at the input surface of the device.
For example, we can simply compress a big volume to a small one while keeping the outside an identical transformation to enhance the field (see Figures 1(a) and (b)), as proposed in [7,20].
Intermediate identical transformations are omitted because of its triviality and to avoid excessive unwieldiness in the material presentation.

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