Explicit μ-bases for conic sections and planar rational cubic curves

• We provide explicit formulas for the μ-bases of conic sections and planar rational cubic curves.
• We derive explicit formulas for the implicit equations and double points of planar rational cubic curves from the μ-bases of planar rational cubic curves.
• We also give explicit formulas for the μ-bases of rational curves of degree n in n-dimensions.

We derive explicit formulas for the μ-bases of conic sections and planar rational cubic curves. Using the μ-bases for planar rational cubic curves, we find explicit formulas for their implicit equations and double points. We also extend the explicit formula for the μ-bases of conic sections to μ-bases for rational curves of degree n in n-dimensions.