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I need to style a raster WMS layer based on a math operation over the raster data. In this case I need to set for example one output channel as a linear ramp from the quotient of the raster data by a constant, and another channel from its remainder.

Is this possible using the SLD file?

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No, it is not, SLD has no such feature, and GeoServer is missing a raster algebra rendering transformation that would do the computation.

If you want to make it happen, see the following: https://github.com/geoserver/geoserver/wiki/Successfully-requesting-and-integrating-new-features-and-improvements-in-GeoServer

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