In the theory of differential forms, a differential ideal I is an algebraic ideal in the ring of smooth differential forms on a smooth manifold, in other words a graded ideal in the sense of ring theory, that is further closed under exterior differentiation d. In other words, for any form α in I, the exterior derivative dα is also in I.
In the theory of differential algebra, a differential ideal I in a differential ring R is an ideal which is mapped to itself by each differential operator.
Read more about Differential Ideal: Exterior Differential Systems and Partial Differential Equations, Perfect Differential Ideals
Famous quotes containing the words differential and/or ideal:
“But how is one to make a scientist understand that there is something unalterably deranged about differential calculus, quantum theory, or the obscene and so inanely liturgical ordeals of the precession of the equinoxes.”
—Antonin Artaud (1896–1948)
“The ideal and the beautiful are identical; the ideal corresponds to the idea, and beauty to form; hence idea and substance are cognate.”
—Victor Hugo (1802–1885)