Big height of an ideal: the largest height of an associated prime. The algorithm is based on the following result by EisenbudHunekeVasconcelos, in their 1993 Inventiones Mathematicae paper:
$\bullet$ codim $Ext^d(M,R) \geq d$ for all $d$
$\bullet$ If $P$ is an associated prime of $M$ of codimension $d :=$ codim $P > $ codim $M$, then codim $Ext^d(M,R) = d$ and the annihilator of $Ext^d(M,R)$ is contained in $P$
$\bullet$ If codim $Ext^d(M,R) = d$, then there really is an associated prime of codimension $d$.



bigHeight works faster than assPrimesHeight
The object bigHeight is a method function.