RandomRegularChainDim0 - Maple Help
For the best experience, we recommend viewing online help using Google Chrome or Microsoft Edge.

RegularChains[FastArithmeticTools]

 RandomRegularChainDim0
 generate a random 0-dim regular chain

 Calling Sequence RandomRegularChainDim0(lv, ld, p)

Parameters

 lv - a list of variables ld - a list of degrees p - a prime number

Description

 • 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.

Examples

 > $\mathrm{with}\left(\mathrm{RegularChains}\right):$
 > $\mathrm{with}\left(\mathrm{ChainTools}\right):$
 > $\mathrm{with}\left(\mathrm{FastArithmeticTools}\right):$
 > $p≔962592769:$
 > $\mathrm{vars}≔\left[\mathrm{x1},\mathrm{x2},\mathrm{x3},\mathrm{x4}\right]:$
 > $R≔\mathrm{PolynomialRing}\left(\mathrm{vars},p\right):$
 > $N≔\mathrm{nops}\left(\mathrm{vars}\right):$
 > $\mathrm{dg}≔3:$
 > $\mathrm{degs}≔\left[\mathrm{seq}\left(4,i=1..N\right)\right]:$
 > $\mathrm{pol}≔\mathrm{randpoly}\left(\mathrm{vars},\mathrm{dense},\mathrm{degree}=\mathrm{dg}\right)+\left(\mathrm{rand}\left(\right)\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}\mathbf{mod}\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}p\right)\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}\mathbf{mod}\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}p:$
 > $\mathrm{tc}≔\mathrm{RandomRegularChainDim0}\left(\mathrm{vars},\mathrm{degs},p\right)$
 ${\mathrm{tc}}{≔}{\mathrm{regular_chain}}$ (1)

Computing with the modpn-supported and modular code

 > $\mathrm{r1}≔\mathrm{IteratedResultantDim0}\left(\mathrm{pol},\mathrm{tc},R\right)$
 ${\mathrm{r1}}{≔}{446889812}$ (2)

Computing with the non-fast non-modular code

 > $\mathrm{r2}≔\mathrm{IteratedResultant}\left(\mathrm{pol},\mathrm{tc},R\right)$
 ${\mathrm{r2}}{≔}{446889812}$ (3)

The results computed by IteratedResultantDim0 and IteratedResultant are equivalent.

 > $\mathrm{evalb}\left(\mathrm{r1}=\mathrm{r2}\right)$
 ${\mathrm{true}}$ (4)