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Is there a way in sage to construct and plot a smooth function which has a given set of data:

• the minima $(miA_1,miA_2)$, $(miB_1,miB_2)$,...
• the maxima $(maA_1,maA_2)$, $(maB_1,maB_2)$,...
• the roots $(nA1,nA2)$, $(nA1,nA2)$...
• a given behaviour for $x \to \pm \infty$.