The command RandomRegularChainDim1 returns a randomly generated one-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.

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

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

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

$p≔962592769\:$

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

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

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

$\mathrm{dg}≔3\:$

$\mathrm{degs}≔\left[\mathrm{seq}\left(2\,i=1..N\right)\right]\:$

$\mathrm{bound}≔3^5\:$

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

$\mathrm{tc}≔\mathrm{RandomRegularChainDim1}\left(\mathrm{vars}\,\mathrm{degs}\,p\right)$

$\mathrm{tc}≔\mathrm{regular\_chain}$

$\mathrm{r1}≔\mathrm{IteratedResultantDim1}\left(\mathrm{pol}\,\mathrm{tc}\,R\,\mathrm{x4}\,\mathrm{bound}\right)$

$\mathrm{r1}≔941032609{\mathrm{x4}}^{24}+942118408{\mathrm{x4}}^{23}+194753142{\mathrm{x4}}^{22}+341712954{\mathrm{x4}}^{21}+2338033{\mathrm{x4}}^{20}+475384741{\mathrm{x4}}^{19}+457989148{\mathrm{x4}}^{18}+681536348{\mathrm{x4}}^{17}+718107114{\mathrm{x4}}^{16}+148212901{\mathrm{x4}}^{15}+33032177{\mathrm{x4}}^{14}+214227263{\mathrm{x4}}^{13}+150959749{\mathrm{x4}}^{12}+8508997{\mathrm{x4}}^{11}+76347793{\mathrm{x4}}^{10}+927296123{\mathrm{x4}}^9+733361705{\mathrm{x4}}^8+689644959{\mathrm{x4}}^7+204369026{\mathrm{x4}}^6+361192708{\mathrm{x4}}^5+138352162{\mathrm{x4}}^4+832291904{\mathrm{x4}}^3+263580044{\mathrm{x4}}^2+106333828\mathrm{x4}+323296554$

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

$\mathrm{r2}≔941032609{\mathrm{x4}}^{24}+942118408{\mathrm{x4}}^{23}+194753142{\mathrm{x4}}^{22}+341712954{\mathrm{x4}}^{21}+2338033{\mathrm{x4}}^{20}+475384741{\mathrm{x4}}^{19}+457989148{\mathrm{x4}}^{18}+681536348{\mathrm{x4}}^{17}+718107114{\mathrm{x4}}^{16}+148212901{\mathrm{x4}}^{15}+33032177{\mathrm{x4}}^{14}+214227263{\mathrm{x4}}^{13}+150959749{\mathrm{x4}}^{12}+8508997{\mathrm{x4}}^{11}+76347793{\mathrm{x4}}^{10}+927296123{\mathrm{x4}}^9+733361705{\mathrm{x4}}^8+689644959{\mathrm{x4}}^7+204369026{\mathrm{x4}}^6+361192708{\mathrm{x4}}^5+138352162{\mathrm{x4}}^4+832291904{\mathrm{x4}}^3+263580044{\mathrm{x4}}^2+106333828\mathrm{x4}+323296554$

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

$\mathrm{true}$