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Formula manipulation

Does Sage have anything similar to Mathematica formula manipulation functions listed below?

Extracting Parts of Formulas: Coefficient ▪ Exponent ▪ Part ▪ Numerator ▪ Denominator

Formula Rearrangement: Collect ▪ Together ▪ Apart ▪ Cancel

Equation Transformations: AddSides ▪ SubtractSides ▪ MultiplySides ▪ DivideSides ▪ ApplySides

Algebraic Transformations: PowerExpand ▪ ComplexExpand ▪ TrigExpand ▪ RootReduce ▪ ComplexityFunction