Abstract We introduce differential primary decompositions for ideals in a commutative ring. Ideal membership is characterized by conditions. The minimal number of conditions needed the arithmetic multiplicity. Minimal are unique up to change bases. Our results generalize construction Noetherian operators analytic theory Ehrenpreis–Palamodov, and they offer concise method representing affine sch...

Noetherian operators are differential that encode primary components of a polynomial ideal. We develop framework, as well algorithms, for computing with local dual spaces, both symbolically and numerically. For ideal, such provide an alternative representation to one given by set generators. This description fits numerical algebraic geometry, taking step toward the goal decomposition.

Hydroxycinnamaldehyde monomers are important intermediates in the lignin biosynthesis and can be incorporated into plants large quantities via genetic modification. They also products formed during pyrolysis or combustion of lignocellulose. In this work, decomposition three hydroxycinnamaldehyde model compounds, cinnamaldehyde, p-coumaraldehyde, coniferaldehyde, was studied a micropyrolysis rea...