Electrodynamics, Curl of P and D

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guiablo
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I know that in statics curl of P=curl of D, since the variation of B in time = 0, and I also know that for linear mediums those curls are 0, but I don't know why, and I don't know if there is any expresion always valid.

I would like to know where this curl comes from like I know where the curl and the divergence of magnetic/inducción/magnetitation field comes so I can picture the electric field in my head easier, as I do with magnetic field, thank you.
 
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I know this is valid always, but i would like to know if we can have the curl of D or P in an expresion that doesn't depend on the other one
 

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