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I want to take geometric intersection of line and polygon shapefile. ArcPy has a tool:

arcpy.Identity_analysis

but it is available with "ArcGIS for Desktop Advanced" and I have "ArcGIS for Desktop Basic".

Is there any alternative tool that I can try?

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    It depends a bit on why do you need to get the geometric intersection - could you describe the scenario in the question? Do you need to combine/transfer attributes? – Alex Tereshenkov Nov 10 '13 at 7:09
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The Intersect tool should provide a suitable alternative.

Both Intersect and Identity perform line-on-polygon overlays but the former keeps only lines sharing a common geography (which includes all geometric intersections) while the latter keeps all lines.

The same tool may be used to perform polygon-on-polygon overlays (with output_type of "LINE") to get line features where polygons intersect.

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