The command RandomRegularChainDim0 returns a randomly generated zero-dimensional regular chain with lv as variables. The degree sequence of the variables is ld. All the coefficients of the polynomials are reduced w.r.t p.

$\mathrm{with}\left(\mathrm{RegularChains}\right)\:$

$\mathrm{with}\left(\mathrm{ChainTools}\right)\:$

$\mathrm{with}\left(\mathrm{FastArithmeticTools}\right)\:$

$p≔962592769\:$

$\mathrm{vars}≔\left[\mathrm{x1}\,\mathrm{x2}\,\mathrm{x3}\,\mathrm{x4}\right]\:$

$R≔\mathrm{PolynomialRing}\left(\mathrm{vars}\,p\right)\:$

$N≔\mathrm{nops}\left(\mathrm{vars}\right)\:$

$\mathrm{dg}≔3\:$

$\mathrm{degs}≔\left[\mathrm{seq}\left(4\,i=1..N\right)\right]\:$

$\mathrm{pol}≔\mathrm{randpoly}\left(\mathrm{vars}\,\mathrm{dense}\,\mathrm{degree}=\mathrm{dg}\right)+\left(\mathrm{rand}\left(\right)\mathbf{mod}p\right)\mathbf{mod}p\:$

$\mathrm{tc}≔\mathrm{RandomRegularChainDim0}\left(\mathrm{vars}\,\mathrm{degs}\,p\right)$

$\mathrm{tc}≔\mathrm{regular\_chain}$

$\mathrm{r1}≔\mathrm{IteratedResultantDim0}\left(\mathrm{pol}\,\mathrm{tc}\,R\right)$

$\mathrm{r1}≔446889812$

$\mathrm{r2}≔\mathrm{IteratedResultant}\left(\mathrm{pol}\,\mathrm{tc}\,R\right)$

$\mathrm{r2}≔446889812$

$\mathrm{evalb}\left(\mathrm{r1}=\mathrm{r2}\right)$

$\mathrm{true}$