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Performing cover operation on a chart-record.

a chart-record,
a list of polynomials from k[S], representatives for elements from k[U], where S comes from the chart, and k[U] is the coordinate ring of the chart.
A list of chart-records.
The elements defined by the parameter CP has to generate the ideal <1> in k[U].

The procedure selects the minimal initial generator set for the ideal of the smallest possible degrees. Then creates a new chart for each remaining generator, in which the zero set of the generator is not part of the chart.

The procedure adopts to the chosen representation of invertible functions (determined by useDEP2).

The input chart is moved to chartHistory and the operation is registered in chartTree. The value of globalChartCounter is increased as needed.

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