(ics,p) = irreducibleCharacteristicSeries I
As we see in the example below, an irreducible characteristic series for $I$ consists of a collection of triangular sets. Here, given a polynomial $f$, write $lvar(f)$ for the largest variable appearing in $f$ (with respect to the lexicographic order). In the example, $lvar(y w+x^2) = y$ . A triangular set consists of polynomials $f_1,\dots,f_r$ such that $lvar(f_1)< \dots < lvar(f_r)$. In the example, $lvar(x*y^2+z^3) = x < w = lvar(w*y+z^2)$ . If $T_1,\dots,T_s$ form an irreducible characteristic series for $I$ , and if $J_i$ is the ideal generated by the largest variables of the elements of $T_i$ , then the algebraic set $V(I)$ defined by $I$ is the union of the sets $V(T_i) \setminus V(I_i)$, for $i=1,\dots,s$. The minimal associated primes of $I$ can thus be recovered from the irreducible characteristic series by saturation and by throwing away superfluous primes. This is done by minimalPrimes, which uses this routine.




The object irreducibleCharacteristicSeries is a method function.