desing v1.5 manual -- An alternative way to resolve reducible algebraic sets

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An alternative way to resolve reducible algebraic sets

The function `desing/dlocext` can be called when there is already a completed resolution stored in chartHistory.

Input:

J: a polynomial from k[VAR], defining the scheme to be desingularized, where VAR is the list of variables of the root chart in the resolution tree stored in chartHistory.

Output:

The value of the resolvedChartList global variable, containing the data of the chart covering the final blowing up variety.

The effect is that the strict transform of J is computed along the map of the resolution which can be found in chartHistory and new basic objects are set up over the leaf-charts of the tree. Then the objects are resolved, such that the existing resolution is "extended" with the resolution of the strict transform of J.

When more than one varieties were resolved using `desing/dlocext` the nonsingular strict transforms (identified by the TAGS) meet in normal crossings. To achieve an embedded resolution of the singularities of the union of all the so resolved varieties, we have to separate these transforms. This is done by `desing/dlocsep`. It works on the resolution stored in chartHistory, and takes no input parameters.