How to find the multiplicity?

By default, the multiplicity is shown next to the field and the number of records that are associated with the current record. If you have customized the column, you can refer to the help documentation to see how to set it up so that it says “X records” instead. If you have set the column to show the number of child records, then the number of records will change when a parent record is updated.

How to find multiplicity of an ideal?

If you want to find the ideal class of an extension, you need to find the ideal class of the original number field first. The ideal class group can be defined in two ways: the usual definition as the set of isomorphism classes of fractional ideals of A whose norms are in the prime ideal class of A, or as the quotient of the group of fractional ideals of A by the subgroup generated by the fractional ideals that are locally principal. The second definition is equivalent

How to find the multiplicity of a maximal ideal?

The answer for this question is rather complicated in the general case as it involves the so-called Hilbert-Samuel multiplicity, an invariant of the ring you are working on. The multiplicity of the maximal ideal in a local ring is the length of its residue field. More generally, it is the length of a certain completion of the local ring.

How to find multiplicity of a decomposition?

In order to determine the multiplicity of the decomposition of a given matrix (or a given linear mapping), we can find the dimension of the kernel of the matrix (or the range of the mapping). This is equivalent to find the dimension of the null space of the matrix (or the kernel of the mapping).

How to find the multiplicity of a decomposition of an ideal?

Even if the ideal $I$ is radical, the multiplicity of a decomposition of $I$ into irreducible ideals need not be $1$. For example, consider the ideal $I = (X^3,X^2Y,XY^2,Y^3)$. There is a primary decomposition for this ideal, but the multiplicities of the primary components are $3$, $2$, $1$, and $3$, respectively, so the total multipl