Performance - Maple Help

Performance

Maple 2019 improves the performance of many routines.

factor

Maple 2019 includes performance improvements for factoring sparse multivariate polynomials with integer coefficients. See factor for more details.

 > $\mathrm{vars}≔\left[\mathrm{seq}\left({x}_{i},i=1..8\right)\right]$
 ${\mathrm{vars}}{≔}\left[{{x}}_{{1}}{,}{{x}}_{{2}}{,}{{x}}_{{3}}{,}{{x}}_{{4}}{,}{{x}}_{{5}}{,}{{x}}_{{6}}{,}{{x}}_{{7}}{,}{{x}}_{{8}}\right]$ (1.1)
 >
 ${g}{≔}{555}{}{{x}}_{{1}}^{{4}}{}{{x}}_{{2}}{}{{x}}_{{3}}^{{2}}{}{{x}}_{{5}}^{{3}}{}{{x}}_{{6}}^{{2}}{}{{x}}_{{7}}{}{{x}}_{{8}}^{{2}}{+}{771}{}{{x}}_{{1}}^{{4}}{}{{x}}_{{2}}{}{{x}}_{{3}}{}{{x}}_{{4}}^{{2}}{}{{x}}_{{6}}^{{3}}{}{{x}}_{{8}}^{{4}}{+}{584}{}{{x}}_{{1}}^{{3}}{}{{x}}_{{2}}{}{{x}}_{{3}}^{{4}}{}{{x}}_{{6}}{}{{x}}_{{7}}^{{6}}{+}{930}{}{{x}}_{{1}}^{{3}}{}{{x}}_{{4}}^{{3}}{}{{x}}_{{5}}{}{{x}}_{{6}}^{{3}}{}{{x}}_{{7}}{}{{x}}_{{8}}^{{4}}{-}{778}{}{{x}}_{{1}}^{{2}}{}{{x}}_{{2}}^{{2}}{}{{x}}_{{3}}{}{{x}}_{{4}}{}{{x}}_{{7}}^{{8}}{}{{x}}_{{8}}{-}{642}{}{{x}}_{{1}}^{{2}}{}{{x}}_{{3}}^{{2}}{}{{x}}_{{4}}^{{2}}{}{{x}}_{{5}}{}{{x}}_{{6}}^{{6}}{}{{x}}_{{7}}{}{{x}}_{{8}}{+}{897}{}{{x}}_{{1}}^{{2}}{}{{x}}_{{4}}^{{2}}{}{{x}}_{{6}}{}{{x}}_{{7}}^{{5}}{}{{x}}_{{8}}^{{5}}{-}{73}{}{{x}}_{{1}}{}{{x}}_{{2}}{}{{x}}_{{3}}^{{4}}{}{{x}}_{{4}}{}{{x}}_{{6}}^{{5}}{}{{x}}_{{7}}{}{{x}}_{{8}}^{{2}}{+}{396}{}{{x}}_{{1}}{}{{x}}_{{2}}{}{{x}}_{{6}}^{{11}}{}{{x}}_{{8}}^{{2}}{+}{728}{}{{x}}_{{2}}^{{6}}{}{{x}}_{{4}}^{{3}}{}{{x}}_{{5}}^{{2}}{}{{x}}_{{6}}{}{{x}}_{{8}}^{{3}}{-}{981}{}{{x}}_{{2}}^{{5}}{}{{x}}_{{3}}{}{{x}}_{{4}}^{{4}}{}{{x}}_{{7}}{}{{x}}_{{8}}^{{4}}{-}{45}{}{{x}}_{{2}}^{{3}}{}{{x}}_{{3}}{}{{x}}_{{4}}^{{4}}{}{{x}}_{{5}}^{{5}}{}{{x}}_{{7}}{}{{x}}_{{8}}{-}{173}{}{{x}}_{{2}}^{{2}}{}{{x}}_{{3}}{}{{x}}_{{4}}^{{3}}{}{{x}}_{{6}}^{{6}}{}{{x}}_{{7}}{}{{x}}_{{8}}^{{2}}{+}{369}{}{{x}}_{{2}}^{{2}}{}{{x}}_{{5}}^{{3}}{}{{x}}_{{6}}^{{4}}{}{{x}}_{{7}}^{{5}}{}{{x}}_{{8}}{+}{190}{}{{x}}_{{2}}{}{{x}}_{{4}}^{{5}}{}{{x}}_{{5}}^{{3}}{}{{x}}_{{7}}{}{{x}}_{{8}}^{{5}}{-}{257}{}{{x}}_{{3}}^{{9}}{}{{x}}_{{5}}^{{2}}{}{{x}}_{{6}}^{{3}}{}{{x}}_{{7}}{+}{227}{}{{x}}_{{3}}^{{2}}{}{{x}}_{{4}}^{{7}}{}{{x}}_{{7}}^{{4}}{}{{x}}_{{8}}^{{2}}{+}{83}{}{{x}}_{{3}}{}{{x}}_{{4}}{}{{x}}_{{6}}^{{11}}{}{{x}}_{{8}}^{{2}}{+}{809}{}{{x}}_{{5}}^{{3}}{}{{x}}_{{6}}{}{{x}}_{{7}}^{{2}}{}{{x}}_{{8}}^{{9}}{-}{921}{}{{x}}_{{1}}^{{6}}{}{{x}}_{{2}}^{{3}}{}{{x}}_{{4}}^{{5}}{-}{466}{}{{x}}_{{1}}^{{2}}{}{{x}}_{{2}}^{{2}}{}{{x}}_{{3}}^{{4}}{}{{x}}_{{6}}{}{{x}}_{{8}}^{{5}}{-}{265}{}{{x}}_{{1}}^{{2}}{}{{x}}_{{2}}^{{2}}{}{{x}}_{{5}}^{{2}}{}{{x}}_{{6}}^{{5}}{}{{x}}_{{7}}^{{2}}{}{{x}}_{{8}}{-}{394}{}{{x}}_{{1}}{}{{x}}_{{2}}{}{{x}}_{{3}}^{{2}}{}{{x}}_{{4}}^{{3}}{}{{x}}_{{5}}^{{2}}{}{{x}}_{{6}}^{{4}}{}{{x}}_{{7}}{+}{898}{}{{x}}_{{1}}{}{{x}}_{{3}}^{{5}}{}{{x}}_{{6}}^{{4}}{}{{x}}_{{7}}^{{2}}{}{{x}}_{{8}}^{{2}}{-}{916}{}{{x}}_{{1}}{}{{x}}_{{4}}{}{{x}}_{{6}}^{{8}}{}{{x}}_{{7}}^{{3}}{}{{x}}_{{8}}{-}{583}{}{{x}}_{{2}}^{{3}}{}{{x}}_{{4}}{}{{x}}_{{5}}^{{8}}{}{{x}}_{{7}}^{{2}}{-}{932}{}{{x}}_{{3}}^{{4}}{}{{x}}_{{7}}^{{10}}{-}{588}{}{{x}}_{{4}}^{{4}}{}{{x}}_{{6}}^{{7}}{}{{x}}_{{7}}^{{2}}{}{{x}}_{{8}}{+}{989}{}{{x}}_{{4}}^{{3}}{}{{x}}_{{5}}^{{6}}{}{{x}}_{{6}}^{{2}}{}{{x}}_{{7}}^{{2}}{}{{x}}_{{8}}{+}{330}{}{{x}}_{{1}}^{{2}}{}{{x}}_{{2}}^{{3}}{}{{x}}_{{4}}{}{{x}}_{{5}}^{{2}}{}{{x}}_{{6}}^{{3}}{}{{x}}_{{8}}^{{2}}{+}{510}{}{{x}}_{{1}}^{{2}}{}{{x}}_{{2}}^{{2}}{}{{x}}_{{4}}^{{2}}{}{{x}}_{{6}}^{{2}}{}{{x}}_{{8}}^{{5}}{+}{587}{}{{x}}_{{1}}^{{2}}{}{{x}}_{{5}}^{{2}}{}{{x}}_{{7}}^{{7}}{}{{x}}_{{8}}^{{2}}{+}{430}{}{{x}}_{{1}}{}{{x}}_{{2}}^{{2}}{}{{x}}_{{4}}^{{6}}{}{{x}}_{{5}}{}{{x}}_{{6}}{}{{x}}_{{7}}^{{2}}{+}{67}{}{{x}}_{{2}}^{{2}}{}{{x}}_{{3}}^{{3}}{}{{x}}_{{4}}^{{3}}{}{{x}}_{{5}}{}{{x}}_{{8}}^{{4}}{-}{296}{}{{x}}_{{1}}^{{3}}{}{{x}}_{{2}}^{{6}}{}{{x}}_{{3}}{}{{x}}_{{4}}{}{{x}}_{{7}}{-}{799}{}{{x}}_{{1}}^{{3}}{}{{x}}_{{2}}{}{{x}}_{{3}}{}{{x}}_{{5}}^{{3}}{}{{x}}_{{7}}^{{3}}{}{{x}}_{{8}}{+}{717}{}{{x}}_{{1}}^{{2}}{}{{x}}_{{2}}^{{5}}{}{{x}}_{{4}}{}{{x}}_{{6}}^{{2}}{}{{x}}_{{8}}^{{2}}{+}{550}{}{{x}}_{{1}}^{{2}}{}{{x}}_{{2}}{}{{x}}_{{5}}^{{2}}{}{{x}}_{{7}}{}{{x}}_{{8}}^{{6}}{-}{417}{}{{x}}_{{1}}^{{2}}{}{{x}}_{{3}}^{{2}}{}{{x}}_{{4}}{}{{x}}_{{5}}^{{4}}{}{{x}}_{{6}}{}{{x}}_{{8}}^{{2}}{-}{991}{}{{x}}_{{2}}^{{7}}{}{{x}}_{{3}}{}{{x}}_{{4}}{}{{x}}_{{5}}^{{2}}{}{{x}}_{{6}}{-}{672}{}{{x}}_{{2}}^{{2}}{}{{x}}_{{3}}^{{2}}{}{{x}}_{{4}}{}{{x}}_{{6}}^{{5}}{}{{x}}_{{7}}^{{2}}{-}{434}{}{{x}}_{{2}}^{{2}}{}{{x}}_{{4}}^{{2}}{}{{x}}_{{5}}{}{{x}}_{{7}}^{{6}}{}{{x}}_{{8}}{+}{399}{}{{x}}_{{2}}^{{2}}{}{{x}}_{{4}}{}{{x}}_{{5}}^{{5}}{}{{x}}_{{6}}{}{{x}}_{{7}}{}{{x}}_{{8}}^{{2}}{-}{23}{}{{x}}_{{2}}{}{{x}}_{{3}}^{{6}}{}{{x}}_{{4}}^{{2}}{}{{x}}_{{6}}{}{{x}}_{{7}}{}{{x}}_{{8}}{-}{500}{}{{x}}_{{1}}^{{5}}{}{{x}}_{{3}}^{{3}}{}{{x}}_{{4}}{}{{x}}_{{5}}^{{2}}{-}{630}{}{{x}}_{{1}}{}{{x}}_{{2}}{}{{x}}_{{3}}{}{{x}}_{{4}}^{{6}}{}{{x}}_{{6}}{}{{x}}_{{7}}{-}{513}{}{{x}}_{{1}}{}{{x}}_{{2}}{}{{x}}_{{3}}{}{{x}}_{{4}}{}{{x}}_{{5}}^{{4}}{}{{x}}_{{7}}{}{{x}}_{{8}}^{{2}}{+}{322}{}{{x}}_{{2}}{}{{x}}_{{4}}^{{3}}{}{{x}}_{{5}}^{{2}}{}{{x}}_{{7}}^{{4}}{}{{x}}_{{8}}{-}{933}{}{{x}}_{{3}}{}{{x}}_{{4}}^{{4}}{}{{x}}_{{5}}^{{3}}{}{{x}}_{{8}}{+}{545}{}{{x}}_{{5}}^{{2}}{}{{x}}_{{6}}{}{{x}}_{{7}}^{{5}}$ (1.2)
 >
 ${h}{≔}{-}{474}{}{{x}}_{{1}}^{{5}}{}{{x}}_{{3}}^{{4}}{}{{x}}_{{4}}^{{3}}{}{{x}}_{{5}}{}{{x}}_{{6}}^{{2}}{+}{429}{}{{x}}_{{1}}^{{4}}{}{{x}}_{{2}}^{{2}}{}{{x}}_{{3}}{}{{x}}_{{6}}^{{4}}{}{{x}}_{{7}}^{{3}}{}{{x}}_{{8}}{-}{188}{}{{x}}_{{1}}^{{3}}{}{{x}}_{{2}}{}{{x}}_{{3}}^{{2}}{}{{x}}_{{4}}^{{3}}{}{{x}}_{{6}}^{{3}}{}{{x}}_{{7}}^{{2}}{}{{x}}_{{8}}{-}{197}{}{{x}}_{{1}}^{{3}}{}{{x}}_{{2}}{}{{x}}_{{3}}{}{{x}}_{{4}}{}{{x}}_{{5}}^{{3}}{}{{x}}_{{6}}^{{3}}{}{{x}}_{{7}}{}{{x}}_{{8}}^{{2}}{-}{464}{}{{x}}_{{1}}^{{2}}{}{{x}}_{{2}}{}{{x}}_{{3}}^{{3}}{}{{x}}_{{4}}^{{3}}{}{{x}}_{{6}}{}{{x}}_{{7}}^{{4}}{}{{x}}_{{8}}{-}{495}{}{{x}}_{{1}}^{{2}}{}{{x}}_{{3}}^{{4}}{}{{x}}_{{5}}{}{{x}}_{{6}}^{{2}}{}{{x}}_{{7}}^{{6}}{+}{725}{}{{x}}_{{1}}{}{{x}}_{{2}}^{{6}}{}{{x}}_{{5}}^{{4}}{}{{x}}_{{7}}^{{4}}{+}{811}{}{{x}}_{{1}}{}{{x}}_{{2}}^{{3}}{}{{x}}_{{3}}{}{{x}}_{{4}}^{{4}}{}{{x}}_{{5}}^{{4}}{}{{x}}_{{6}}{}{{x}}_{{7}}{-}{26}{}{{x}}_{{1}}{}{{x}}_{{2}}{}{{x}}_{{3}}^{{3}}{}{{x}}_{{4}}^{{4}}{}{{x}}_{{5}}^{{2}}{}{{x}}_{{6}}{}{{x}}_{{7}}^{{3}}{+}{470}{}{{x}}_{{2}}^{{3}}{}{{x}}_{{5}}^{{7}}{}{{x}}_{{7}}^{{3}}{}{{x}}_{{8}}^{{2}}{+}{159}{}{{x}}_{{2}}{}{{x}}_{{3}}^{{4}}{}{{x}}_{{5}}^{{4}}{}{{x}}_{{8}}^{{6}}{-}{631}{}{{x}}_{{1}}^{{5}}{}{{x}}_{{2}}^{{3}}{}{{x}}_{{3}}{}{{x}}_{{4}}^{{4}}{}{{x}}_{{7}}{-}{910}{}{{x}}_{{1}}^{{4}}{}{{x}}_{{4}}^{{3}}{}{{x}}_{{6}}{}{{x}}_{{7}}^{{4}}{}{{x}}_{{8}}^{{2}}{+}{527}{}{{x}}_{{1}}^{{3}}{}{{x}}_{{2}}{}{{x}}_{{3}}^{{5}}{}{{x}}_{{5}}^{{2}}{}{{x}}_{{8}}^{{3}}{+}{558}{}{{x}}_{{1}}^{{3}}{}{{x}}_{{2}}{}{{x}}_{{3}}^{{3}}{}{{x}}_{{4}}^{{5}}{}{{x}}_{{7}}^{{2}}{-}{168}{}{{x}}_{{1}}^{{3}}{}{{x}}_{{4}}^{{4}}{}{{x}}_{{6}}^{{3}}{}{{x}}_{{8}}^{{4}}{+}{920}{}{{x}}_{{1}}^{{2}}{}{{x}}_{{2}}^{{6}}{}{{x}}_{{4}}^{{2}}{}{{x}}_{{7}}^{{3}}{}{{x}}_{{8}}{-}{672}{}{{x}}_{{1}}{}{{x}}_{{2}}^{{4}}{}{{x}}_{{4}}^{{3}}{}{{x}}_{{6}}^{{5}}{}{{x}}_{{8}}{+}{201}{}{{x}}_{{1}}{}{{x}}_{{2}}^{{2}}{}{{x}}_{{4}}^{{9}}{}{{x}}_{{6}}{}{{x}}_{{8}}{+}{660}{}{{x}}_{{1}}{}{{x}}_{{2}}{}{{x}}_{{5}}^{{6}}{}{{x}}_{{6}}^{{5}}{}{{x}}_{{7}}{+}{153}{}{{x}}_{{1}}{}{{x}}_{{5}}^{{8}}{}{{x}}_{{7}}^{{2}}{}{{x}}_{{8}}^{{3}}{-}{628}{}{{x}}_{{2}}^{{6}}{}{{x}}_{{3}}{}{{x}}_{{4}}^{{3}}{}{{x}}_{{5}}^{{3}}{}{{x}}_{{8}}{+}{771}{}{{x}}_{{2}}^{{3}}{}{{x}}_{{4}}^{{2}}{}{{x}}_{{5}}^{{9}}{-}{710}{}{{x}}_{{2}}^{{2}}{}{{x}}_{{4}}^{{6}}{}{{x}}_{{5}}^{{2}}{}{{x}}_{{7}}^{{4}}{+}{392}{}{{x}}_{{2}}^{{2}}{}{{x}}_{{5}}^{{7}}{}{{x}}_{{8}}^{{5}}{+}{211}{}{{x}}_{{2}}{}{{x}}_{{4}}^{{6}}{}{{x}}_{{5}}{}{{x}}_{{6}}^{{3}}{}{{x}}_{{8}}^{{3}}{-}{997}{}{{x}}_{{3}}^{{3}}{}{{x}}_{{4}}{}{{x}}_{{5}}^{{5}}{}{{x}}_{{6}}^{{2}}{}{{x}}_{{7}}{}{{x}}_{{8}}^{{2}}{-}{968}{}{{x}}_{{3}}{}{{x}}_{{5}}{}{{x}}_{{7}}^{{12}}{-}{160}{}{{x}}_{{1}}^{{4}}{}{{x}}_{{2}}^{{2}}{}{{x}}_{{5}}^{{2}}{}{{x}}_{{8}}^{{5}}{-}{488}{}{{x}}_{{1}}^{{3}}{}{{x}}_{{3}}{}{{x}}_{{5}}^{{2}}{}{{x}}_{{7}}^{{7}}{+}{554}{}{{x}}_{{1}}^{{2}}{}{{x}}_{{2}}^{{2}}{}{{x}}_{{3}}^{{3}}{}{{x}}_{{4}}^{{6}}{-}{687}{}{{x}}_{{1}}^{{2}}{}{{x}}_{{2}}{}{{x}}_{{4}}^{{2}}{}{{x}}_{{5}}{}{{x}}_{{6}}^{{3}}{}{{x}}_{{7}}^{{2}}{}{{x}}_{{8}}^{{2}}{+}{665}{}{{x}}_{{1}}{}{{x}}_{{2}}^{{3}}{}{{x}}_{{3}}^{{3}}{}{{x}}_{{4}}^{{3}}{}{{x}}_{{8}}^{{3}}{+}{870}{}{{x}}_{{2}}^{{2}}{}{{x}}_{{3}}^{{6}}{}{{x}}_{{5}}^{{3}}{}{{x}}_{{7}}{}{{x}}_{{8}}{-}{160}{}{{x}}_{{2}}^{{2}}{}{{x}}_{{5}}^{{4}}{}{{x}}_{{7}}^{{7}}{+}{136}{}{{x}}_{{2}}{}{{x}}_{{3}}^{{2}}{}{{x}}_{{4}}^{{2}}{}{{x}}_{{6}}{}{{x}}_{{7}}^{{6}}{}{{x}}_{{8}}{-}{487}{}{{x}}_{{1}}^{{4}}{}{{x}}_{{2}}{}{{x}}_{{3}}^{{5}}{}{{x}}_{{5}}{}{{x}}_{{8}}{+}{549}{}{{x}}_{{1}}{}{{x}}_{{2}}^{{3}}{}{{x}}_{{3}}^{{2}}{}{{x}}_{{4}}^{{3}}{}{{x}}_{{5}}{}{{x}}_{{6}}^{{2}}{-}{262}{}{{x}}_{{1}}{}{{x}}_{{2}}^{{2}}{}{{x}}_{{6}}^{{4}}{}{{x}}_{{7}}{}{{x}}_{{8}}^{{4}}{+}{649}{}{{x}}_{{1}}{}{{x}}_{{2}}{}{{x}}_{{3}}^{{2}}{}{{x}}_{{4}}^{{4}}{}{{x}}_{{6}}^{{2}}{}{{x}}_{{8}}^{{2}}{+}{864}{}{{x}}_{{1}}{}{{x}}_{{2}}{}{{x}}_{{3}}^{{2}}{}{{x}}_{{4}}^{{2}}{}{{x}}_{{6}}^{{3}}{}{{x}}_{{7}}{}{{x}}_{{8}}^{{2}}{+}{336}{}{{x}}_{{1}}^{{3}}{}{{x}}_{{2}}{}{{x}}_{{3}}^{{2}}{}{{x}}_{{4}}^{{2}}{}{{x}}_{{6}}{}{{x}}_{{7}}{}{{x}}_{{8}}{-}{679}{}{{x}}_{{1}}{}{{x}}_{{2}}{}{{x}}_{{3}}^{{3}}{}{{x}}_{{4}}{}{{x}}_{{5}}^{{3}}{}{{x}}_{{7}}{}{{x}}_{{8}}{+}{871}{}{{x}}_{{2}}^{{2}}{}{{x}}_{{3}}^{{7}}{}{{x}}_{{4}}{}{{x}}_{{7}}{-}{823}{}{{x}}_{{3}}^{{3}}{}{{x}}_{{4}}^{{6}}{}{{x}}_{{6}}{}{{x}}_{{8}}{+}{386}{}{{x}}_{{1}}{}{{x}}_{{2}}^{{2}}{}{{x}}_{{6}}^{{3}}{}{{x}}_{{7}}{}{{x}}_{{8}}^{{3}}{-}{373}{}{{x}}_{{2}}{}{{x}}_{{5}}^{{4}}{}{{x}}_{{6}}^{{3}}{}{{x}}_{{8}}{+}{511}{}{{x}}_{{1}}^{{2}}{}{{x}}_{{2}}{}{{x}}_{{4}}{}{{x}}_{{7}}^{{2}}{}{{x}}_{{8}}^{{2}}{-}{838}{}{{x}}_{{2}}^{{2}}{}{{x}}_{{6}}{}{{x}}_{{7}}^{{4}}{}{{x}}_{{8}}{-}{124}{}{{x}}_{{2}}^{{3}}{}{{x}}_{{4}}{}{{x}}_{{5}}{}{{x}}_{{7}}$ (1.3)
 > $f≔\mathrm{expand}\left(g\cdot h\right):$

The following factorization took about 5 seconds in Maple 2018 on the same machine.

 > $\mathrm{CodeTools}:-\mathrm{Usage}\left(\mathrm{factor}\left(f\right)\right)$
 memory used=40.03MiB, alloc change=41.09MiB, cpu time=250.00ms, real time=247.00ms, gc time=0ns
 $\left({474}{}{{x}}_{{1}}^{{5}}{}{{x}}_{{3}}^{{4}}{}{{x}}_{{4}}^{{3}}{}{{x}}_{{5}}{}{{x}}_{{6}}^{{2}}{-}{429}{}{{x}}_{{1}}^{{4}}{}{{x}}_{{2}}^{{2}}{}{{x}}_{{3}}{}{{x}}_{{6}}^{{4}}{}{{x}}_{{7}}^{{3}}{}{{x}}_{{8}}{+}{188}{}{{x}}_{{1}}^{{3}}{}{{x}}_{{2}}{}{{x}}_{{3}}^{{2}}{}{{x}}_{{4}}^{{3}}{}{{x}}_{{6}}^{{3}}{}{{x}}_{{7}}^{{2}}{}{{x}}_{{8}}{+}{197}{}{{x}}_{{1}}^{{3}}{}{{x}}_{{2}}{}{{x}}_{{3}}{}{{x}}_{{4}}{}{{x}}_{{5}}^{{3}}{}{{x}}_{{6}}^{{3}}{}{{x}}_{{7}}{}{{x}}_{{8}}^{{2}}{+}{464}{}{{x}}_{{1}}^{{2}}{}{{x}}_{{2}}{}{{x}}_{{3}}^{{3}}{}{{x}}_{{4}}^{{3}}{}{{x}}_{{6}}{}{{x}}_{{7}}^{{4}}{}{{x}}_{{8}}{+}{495}{}{{x}}_{{1}}^{{2}}{}{{x}}_{{3}}^{{4}}{}{{x}}_{{5}}{}{{x}}_{{6}}^{{2}}{}{{x}}_{{7}}^{{6}}{-}{725}{}{{x}}_{{1}}{}{{x}}_{{2}}^{{6}}{}{{x}}_{{5}}^{{4}}{}{{x}}_{{7}}^{{4}}{-}{811}{}{{x}}_{{1}}{}{{x}}_{{2}}^{{3}}{}{{x}}_{{3}}{}{{x}}_{{4}}^{{4}}{}{{x}}_{{5}}^{{4}}{}{{x}}_{{6}}{}{{x}}_{{7}}{+}{26}{}{{x}}_{{1}}{}{{x}}_{{2}}{}{{x}}_{{3}}^{{3}}{}{{x}}_{{4}}^{{4}}{}{{x}}_{{5}}^{{2}}{}{{x}}_{{6}}{}{{x}}_{{7}}^{{3}}{-}{470}{}{{x}}_{{2}}^{{3}}{}{{x}}_{{5}}^{{7}}{}{{x}}_{{7}}^{{3}}{}{{x}}_{{8}}^{{2}}{-}{159}{}{{x}}_{{2}}{}{{x}}_{{3}}^{{4}}{}{{x}}_{{5}}^{{4}}{}{{x}}_{{8}}^{{6}}{+}{631}{}{{x}}_{{1}}^{{5}}{}{{x}}_{{2}}^{{3}}{}{{x}}_{{3}}{}{{x}}_{{4}}^{{4}}{}{{x}}_{{7}}{+}{910}{}{{x}}_{{1}}^{{4}}{}{{x}}_{{4}}^{{3}}{}{{x}}_{{6}}{}{{x}}_{{7}}^{{4}}{}{{x}}_{{8}}^{{2}}{-}{527}{}{{x}}_{{1}}^{{3}}{}{{x}}_{{2}}{}{{x}}_{{3}}^{{5}}{}{{x}}_{{5}}^{{2}}{}{{x}}_{{8}}^{{3}}{-}{558}{}{{x}}_{{1}}^{{3}}{}{{x}}_{{2}}{}{{x}}_{{3}}^{{3}}{}{{x}}_{{4}}^{{5}}{}{{x}}_{{7}}^{{2}}{+}{168}{}{{x}}_{{1}}^{{3}}{}{{x}}_{{4}}^{{4}}{}{{x}}_{{6}}^{{3}}{}{{x}}_{{8}}^{{4}}{-}{920}{}{{x}}_{{1}}^{{2}}{}{{x}}_{{2}}^{{6}}{}{{x}}_{{4}}^{{2}}{}{{x}}_{{7}}^{{3}}{}{{x}}_{{8}}{+}{672}{}{{x}}_{{1}}{}{{x}}_{{2}}^{{4}}{}{{x}}_{{4}}^{{3}}{}{{x}}_{{6}}^{{5}}{}{{x}}_{{8}}{-}{201}{}{{x}}_{{1}}{}{{x}}_{{2}}^{{2}}{}{{x}}_{{4}}^{{9}}{}{{x}}_{{6}}{}{{x}}_{{8}}{-}{660}{}{{x}}_{{1}}{}{{x}}_{{2}}{}{{x}}_{{5}}^{{6}}{}{{x}}_{{6}}^{{5}}{}{{x}}_{{7}}{-}{153}{}{{x}}_{{1}}{}{{x}}_{{5}}^{{8}}{}{{x}}_{{7}}^{{2}}{}{{x}}_{{8}}^{{3}}{+}{628}{}{{x}}_{{2}}^{{6}}{}{{x}}_{{3}}{}{{x}}_{{4}}^{{3}}{}{{x}}_{{5}}^{{3}}{}{{x}}_{{8}}{-}{771}{}{{x}}_{{2}}^{{3}}{}{{x}}_{{4}}^{{2}}{}{{x}}_{{5}}^{{9}}{+}{710}{}{{x}}_{{2}}^{{2}}{}{{x}}_{{4}}^{{6}}{}{{x}}_{{5}}^{{2}}{}{{x}}_{{7}}^{{4}}{-}{392}{}{{x}}_{{2}}^{{2}}{}{{x}}_{{5}}^{{7}}{}{{x}}_{{8}}^{{5}}{-}{211}{}{{x}}_{{2}}{}{{x}}_{{4}}^{{6}}{}{{x}}_{{5}}{}{{x}}_{{6}}^{{3}}{}{{x}}_{{8}}^{{3}}{+}{997}{}{{x}}_{{3}}^{{3}}{}{{x}}_{{4}}{}{{x}}_{{5}}^{{5}}{}{{x}}_{{6}}^{{2}}{}{{x}}_{{7}}{}{{x}}_{{8}}^{{2}}{+}{968}{}{{x}}_{{3}}{}{{x}}_{{5}}{}{{x}}_{{7}}^{{12}}{+}{160}{}{{x}}_{{1}}^{{4}}{}{{x}}_{{2}}^{{2}}{}{{x}}_{{5}}^{{2}}{}{{x}}_{{8}}^{{5}}{+}{488}{}{{x}}_{{1}}^{{3}}{}{{x}}_{{3}}{}{{x}}_{{5}}^{{2}}{}{{x}}_{{7}}^{{7}}{-}{554}{}{{x}}_{{1}}^{{2}}{}{{x}}_{{2}}^{{2}}{}{{x}}_{{3}}^{{3}}{}{{x}}_{{4}}^{{6}}{+}{687}{}{{x}}_{{1}}^{{2}}{}{{x}}_{{2}}{}{{x}}_{{4}}^{{2}}{}{{x}}_{{5}}{}{{x}}_{{6}}^{{3}}{}{{x}}_{{7}}^{{2}}{}{{x}}_{{8}}^{{2}}{-}{665}{}{{x}}_{{1}}{}{{x}}_{{2}}^{{3}}{}{{x}}_{{3}}^{{3}}{}{{x}}_{{4}}^{{3}}{}{{x}}_{{8}}^{{3}}{-}{870}{}{{x}}_{{2}}^{{2}}{}{{x}}_{{3}}^{{6}}{}{{x}}_{{5}}^{{3}}{}{{x}}_{{7}}{}{{x}}_{{8}}{+}{160}{}{{x}}_{{2}}^{{2}}{}{{x}}_{{5}}^{{4}}{}{{x}}_{{7}}^{{7}}{-}{136}{}{{x}}_{{2}}{}{{x}}_{{3}}^{{2}}{}{{x}}_{{4}}^{{2}}{}{{x}}_{{6}}{}{{x}}_{{7}}^{{6}}{}{{x}}_{{8}}{+}{487}{}{{x}}_{{1}}^{{4}}{}{{x}}_{{2}}{}{{x}}_{{3}}^{{5}}{}{{x}}_{{5}}{}{{x}}_{{8}}{-}{549}{}{{x}}_{{1}}{}{{x}}_{{2}}^{{3}}{}{{x}}_{{3}}^{{2}}{}{{x}}_{{4}}^{{3}}{}{{x}}_{{5}}{}{{x}}_{{6}}^{{2}}{+}{262}{}{{x}}_{{1}}{}{{x}}_{{2}}^{{2}}{}{{x}}_{{6}}^{{4}}{}{{x}}_{{7}}{}{{x}}_{{8}}^{{4}}{-}{649}{}{{x}}_{{1}}{}{{x}}_{{2}}{}{{x}}_{{3}}^{{2}}{}{{x}}_{{4}}^{{4}}{}{{x}}_{{6}}^{{2}}{}{{x}}_{{8}}^{{2}}{-}{864}{}{{x}}_{{1}}{}{{x}}_{{2}}{}{{x}}_{{3}}^{{2}}{}{{x}}_{{4}}^{{2}}{}{{x}}_{{6}}^{{3}}{}{{x}}_{{7}}{}{{x}}_{{8}}^{{2}}{-}{336}{}{{x}}_{{1}}^{{3}}{}{{x}}_{{2}}{}{{x}}_{{3}}^{{2}}{}{{x}}_{{4}}^{{2}}{}{{x}}_{{6}}{}{{x}}_{{7}}{}{{x}}_{{8}}{+}{679}{}{{x}}_{{1}}{}{{x}}_{{2}}{}{{x}}_{{3}}^{{3}}{}{{x}}_{{4}}{}{{x}}_{{5}}^{{3}}{}{{x}}_{{7}}{}{{x}}_{{8}}{-}{871}{}{{x}}_{{2}}^{{2}}{}{{x}}_{{3}}^{{7}}{}{{x}}_{{4}}{}{{x}}_{{7}}{+}{823}{}{{x}}_{{3}}^{{3}}{}{{x}}_{{4}}^{{6}}{}{{x}}_{{6}}{}{{x}}_{{8}}{-}{386}{}{{x}}_{{1}}{}{{x}}_{{2}}^{{2}}{}{{x}}_{{6}}^{{3}}{}{{x}}_{{7}}{}{{x}}_{{8}}^{{3}}{+}{373}{}{{x}}_{{2}}{}{{x}}_{{5}}^{{4}}{}{{x}}_{{6}}^{{3}}{}{{x}}_{{8}}{-}{511}{}{{x}}_{{1}}^{{2}}{}{{x}}_{{2}}{}{{x}}_{{4}}{}{{x}}_{{7}}^{{2}}{}{{x}}_{{8}}^{{2}}{+}{838}{}{{x}}_{{2}}^{{2}}{}{{x}}_{{6}}{}{{x}}_{{7}}^{{4}}{}{{x}}_{{8}}{+}{124}{}{{x}}_{{2}}^{{3}}{}{{x}}_{{4}}{}{{x}}_{{5}}{}{{x}}_{{7}}\right){}\left({-}{555}{}{{x}}_{{1}}^{{4}}{}{{x}}_{{2}}{}{{x}}_{{3}}^{{2}}{}{{x}}_{{5}}^{{3}}{}{{x}}_{{6}}^{{2}}{}{{x}}_{{7}}{}{{x}}_{{8}}^{{2}}{-}{771}{}{{x}}_{{1}}^{{4}}{}{{x}}_{{2}}{}{{x}}_{{3}}{}{{x}}_{{4}}^{{2}}{}{{x}}_{{6}}^{{3}}{}{{x}}_{{8}}^{{4}}{-}{584}{}{{x}}_{{1}}^{{3}}{}{{x}}_{{2}}{}{{x}}_{{3}}^{{4}}{}{{x}}_{{6}}{}{{x}}_{{7}}^{{6}}{-}{930}{}{{x}}_{{1}}^{{3}}{}{{x}}_{{4}}^{{3}}{}{{x}}_{{5}}{}{{x}}_{{6}}^{{3}}{}{{x}}_{{7}}{}{{x}}_{{8}}^{{4}}{+}{778}{}{{x}}_{{1}}^{{2}}{}{{x}}_{{2}}^{{2}}{}{{x}}_{{3}}{}{{x}}_{{4}}{}{{x}}_{{7}}^{{8}}{}{{x}}_{{8}}{+}{642}{}{{x}}_{{1}}^{{2}}{}{{x}}_{{3}}^{{2}}{}{{x}}_{{4}}^{{2}}{}{{x}}_{{5}}{}{{x}}_{{6}}^{{6}}{}{{x}}_{{7}}{}{{x}}_{{8}}{-}{897}{}{{x}}_{{1}}^{{2}}{}{{x}}_{{4}}^{{2}}{}{{x}}_{{6}}{}{{x}}_{{7}}^{{5}}{}{{x}}_{{8}}^{{5}}{+}{73}{}{{x}}_{{1}}{}{{x}}_{{2}}{}{{x}}_{{3}}^{{4}}{}{{x}}_{{4}}{}{{x}}_{{6}}^{{5}}{}{{x}}_{{7}}{}{{x}}_{{8}}^{{2}}{-}{396}{}{{x}}_{{1}}{}{{x}}_{{2}}{}{{x}}_{{6}}^{{11}}{}{{x}}_{{8}}^{{2}}{-}{728}{}{{x}}_{{2}}^{{6}}{}{{x}}_{{4}}^{{3}}{}{{x}}_{{5}}^{{2}}{}{{x}}_{{6}}{}{{x}}_{{8}}^{{3}}{+}{981}{}{{x}}_{{2}}^{{5}}{}{{x}}_{{3}}{}{{x}}_{{4}}^{{4}}{}{{x}}_{{7}}{}{{x}}_{{8}}^{{4}}{+}{45}{}{{x}}_{{2}}^{{3}}{}{{x}}_{{3}}{}{{x}}_{{4}}^{{4}}{}{{x}}_{{5}}^{{5}}{}{{x}}_{{7}}{}{{x}}_{{8}}{+}{173}{}{{x}}_{{2}}^{{2}}{}{{x}}_{{3}}{}{{x}}_{{4}}^{{3}}{}{{x}}_{{6}}^{{6}}{}{{x}}_{{7}}{}{{x}}_{{8}}^{{2}}{-}{369}{}{{x}}_{{2}}^{{2}}{}{{x}}_{{5}}^{{3}}{}{{x}}_{{6}}^{{4}}{}{{x}}_{{7}}^{{5}}{}{{x}}_{{8}}{-}{190}{}{{x}}_{{2}}{}{{x}}_{{4}}^{{5}}{}{{x}}_{{5}}^{{3}}{}{{x}}_{{7}}{}{{x}}_{{8}}^{{5}}{+}{257}{}{{x}}_{{3}}^{{9}}{}{{x}}_{{5}}^{{2}}{}{{x}}_{{6}}^{{3}}{}{{x}}_{{7}}{-}{227}{}{{x}}_{{3}}^{{2}}{}{{x}}_{{4}}^{{7}}{}{{x}}_{{7}}^{{4}}{}{{x}}_{{8}}^{{2}}{-}{83}{}{{x}}_{{3}}{}{{x}}_{{4}}{}{{x}}_{{6}}^{{11}}{}{{x}}_{{8}}^{{2}}{-}{809}{}{{x}}_{{5}}^{{3}}{}{{x}}_{{6}}{}{{x}}_{{7}}^{{2}}{}{{x}}_{{8}}^{{9}}{+}{921}{}{{x}}_{{1}}^{{6}}{}{{x}}_{{2}}^{{3}}{}{{x}}_{{4}}^{{5}}{+}{466}{}{{x}}_{{1}}^{{2}}{}{{x}}_{{2}}^{{2}}{}{{x}}_{{3}}^{{4}}{}{{x}}_{{6}}{}{{x}}_{{8}}^{{5}}{+}{265}{}{{x}}_{{1}}^{{2}}{}{{x}}_{{2}}^{{2}}{}{{x}}_{{5}}^{{2}}{}{{x}}_{{6}}^{{5}}{}{{x}}_{{7}}^{{2}}{}{{x}}_{{8}}{+}{394}{}{{x}}_{{1}}{}{{x}}_{{2}}{}{{x}}_{{3}}^{{2}}{}{{x}}_{{4}}^{{3}}{}{{x}}_{{5}}^{{2}}{}{{x}}_{{6}}^{{4}}{}{{x}}_{{7}}{-}{898}{}{{x}}_{{1}}{}{{x}}_{{3}}^{{5}}{}{{x}}_{{6}}^{{4}}{}{{x}}_{{7}}^{{2}}{}{{x}}_{{8}}^{{2}}{+}{916}{}{{x}}_{{1}}{}{{x}}_{{4}}{}{{x}}_{{6}}^{{8}}{}{{x}}_{{7}}^{{3}}{}{{x}}_{{8}}{+}{583}{}{{x}}_{{2}}^{{3}}{}{{x}}_{{4}}{}{{x}}_{{5}}^{{8}}{}{{x}}_{{7}}^{{2}}{+}{932}{}{{x}}_{{3}}^{{4}}{}{{x}}_{{7}}^{{10}}{+}{588}{}{{x}}_{{4}}^{{4}}{}{{x}}_{{6}}^{{7}}{}{{x}}_{{7}}^{{2}}{}{{x}}_{{8}}{-}{989}{}{{x}}_{{4}}^{{3}}{}{{x}}_{{5}}^{{6}}{}{{x}}_{{6}}^{{2}}{}{{x}}_{{7}}^{{2}}{}{{x}}_{{8}}{-}{330}{}{{x}}_{{1}}^{{2}}{}{{x}}_{{2}}^{{3}}{}{{x}}_{{4}}{}{{x}}_{{5}}^{{2}}{}{{x}}_{{6}}^{{3}}{}{{x}}_{{8}}^{{2}}{-}{510}{}{{x}}_{{1}}^{{2}}{}{{x}}_{{2}}^{{2}}{}{{x}}_{{4}}^{{2}}{}{{x}}_{{6}}^{{2}}{}{{x}}_{{8}}^{{5}}{-}{587}{}{{x}}_{{1}}^{{2}}{}{{x}}_{{5}}^{{2}}{}{{x}}_{{7}}^{{7}}{}{{x}}_{{8}}^{{2}}{-}{430}{}{{x}}_{{1}}{}{{x}}_{{2}}^{{2}}{}{{x}}_{{4}}^{{6}}{}{{x}}_{{5}}{}{{x}}_{{6}}{}{{x}}_{{7}}^{{2}}{-}{67}{}{{x}}_{{2}}^{{2}}{}{{x}}_{{3}}^{{3}}{}{{x}}_{{4}}^{{3}}{}{{x}}_{{5}}{}{{x}}_{{8}}^{{4}}{+}{296}{}{{x}}_{{1}}^{{3}}{}{{x}}_{{2}}^{{6}}{}{{x}}_{{3}}{}{{x}}_{{4}}{}{{x}}_{{7}}{+}{799}{}{{x}}_{{1}}^{{3}}{}{{x}}_{{2}}{}{{x}}_{{3}}{}{{x}}_{{5}}^{{3}}{}{{x}}_{{7}}^{{3}}{}{{x}}_{{8}}{-}{717}{}{{x}}_{{1}}^{{2}}{}{{x}}_{{2}}^{{5}}{}{{x}}_{{4}}{}{{x}}_{{6}}^{{2}}{}{{x}}_{{8}}^{{2}}{-}{550}{}{{x}}_{{1}}^{{2}}{}{{x}}_{{2}}{}{{x}}_{{5}}^{{2}}{}{{x}}_{{7}}{}{{x}}_{{8}}^{{6}}{+}{417}{}{{x}}_{{1}}^{{2}}{}{{x}}_{{3}}^{{2}}{}{{x}}_{{4}}{}{{x}}_{{5}}^{{4}}{}{{x}}_{{6}}{}{{x}}_{{8}}^{{2}}{+}{991}{}{{x}}_{{2}}^{{7}}{}{{x}}_{{3}}{}{{x}}_{{4}}{}{{x}}_{{5}}^{{2}}{}{{x}}_{{6}}{+}{672}{}{{x}}_{{2}}^{{2}}{}{{x}}_{{3}}^{{2}}{}{{x}}_{{4}}{}{{x}}_{{6}}^{{5}}{}{{x}}_{{7}}^{{2}}{+}{434}{}{{x}}_{{2}}^{{2}}{}{{x}}_{{4}}^{{2}}{}{{x}}_{{5}}{}{{x}}_{{7}}^{{6}}{}{{x}}_{{8}}{-}{399}{}{{x}}_{{2}}^{{2}}{}{{x}}_{{4}}{}{{x}}_{{5}}^{{5}}{}{{x}}_{{6}}{}{{x}}_{{7}}{}{{x}}_{{8}}^{{2}}{+}{23}{}{{x}}_{{2}}{}{{x}}_{{3}}^{{6}}{}{{x}}_{{4}}^{{2}}{}{{x}}_{{6}}{}{{x}}_{{7}}{}{{x}}_{{8}}{+}{500}{}{{x}}_{{1}}^{{5}}{}{{x}}_{{3}}^{{3}}{}{{x}}_{{4}}{}{{x}}_{{5}}^{{2}}{+}{630}{}{{x}}_{{1}}{}{{x}}_{{2}}{}{{x}}_{{3}}{}{{x}}_{{4}}^{{6}}{}{{x}}_{{6}}{}{{x}}_{{7}}{+}{513}{}{{x}}_{{1}}{}{{x}}_{{2}}{}{{x}}_{{3}}{}{{x}}_{{4}}{}{{x}}_{{5}}^{{4}}{}{{x}}_{{7}}{}{{x}}_{{8}}^{{2}}{-}{322}{}{{x}}_{{2}}{}{{x}}_{{4}}^{{3}}{}{{x}}_{{5}}^{{2}}{}{{x}}_{{7}}^{{4}}{}{{x}}_{{8}}{+}{933}{}{{x}}_{{3}}{}{{x}}_{{4}}^{{4}}{}{{x}}_{{5}}^{{3}}{}{{x}}_{{8}}{-}{545}{}{{x}}_{{5}}^{{2}}{}{{x}}_{{6}}{}{{x}}_{{7}}^{{5}}\right)$ (1.4)

A larger example, with about 30000 terms.

 > $f≔\mathrm{expand}\left(\mathrm{mul}\left(\mathrm{randpoly}\left(\left[\mathrm{seq}\left({x}_{j},j=1..12\right)\right],\mathrm{degree}=15,\mathrm{terms}=30,\mathrm{coeffs}=\mathrm{rand}\left(1..100000\right)\right)+i,i=1..3\right)\right):$
 > $\mathrm{nops}\left(f\right)$
 ${29791}$ (1.5)

This factorization took more than 1 minute in Maple 2018.

 > $F≔\mathrm{CodeTools}:-\mathrm{Usage}\left(\mathrm{factor}\left(f\right)\right):$
 memory used=475.20MiB, alloc change=133.50MiB, cpu time=3.29s, real time=3.08s, gc time=468.00ms
 > $\mathrm{nops}\left(F\right)$
 ${3}$ (1.6)

The last example is the determinant of a generic circulant matrix, i.e., where all entries are indeterminates, and each row is a cyclic rotation of the first one.

 >
 > $A≔\mathrm{Matrix}\left(12,\mathrm{shape}=\mathrm{Circulant}\left[\left[\mathrm{seq}\left({x}_{j},j=1..12\right)\right]\right]\right)$
 $\left[\begin{array}{cccccccccccc}{x}_{1}& {x}_{2}& {x}_{3}& {x}_{4}& {x}_{5}& {x}_{6}& {x}_{7}& {x}_{8}& {x}_{9}& {x}_{10}& {x}_{11}& {x}_{12}\\ {x}_{12}& {x}_{1}& {x}_{2}& {x}_{3}& {x}_{4}& {x}_{5}& {x}_{6}& {x}_{7}& {x}_{8}& {x}_{9}& {x}_{10}& {x}_{11}\\ {x}_{11}& {x}_{12}& {x}_{1}& {x}_{2}& {x}_{3}& {x}_{4}& {x}_{5}& {x}_{6}& {x}_{7}& {x}_{8}& {x}_{9}& {x}_{10}\\ {x}_{10}& {x}_{11}& {x}_{12}& {x}_{1}& {x}_{2}& {x}_{3}& {x}_{4}& {x}_{5}& {x}_{6}& {x}_{7}& {x}_{8}& {x}_{9}\\ {x}_{9}& {x}_{10}& {x}_{11}& {x}_{12}& {x}_{1}& {x}_{2}& {x}_{3}& {x}_{4}& {x}_{5}& {x}_{6}& {x}_{7}& {x}_{8}\\ {x}_{8}& {x}_{9}& {x}_{10}& {x}_{11}& {x}_{12}& {x}_{1}& {x}_{2}& {x}_{3}& {x}_{4}& {x}_{5}& {x}_{6}& {x}_{7}\\ {x}_{7}& {x}_{8}& {x}_{9}& {x}_{10}& {x}_{11}& {x}_{12}& {x}_{1}& {x}_{2}& {x}_{3}& {x}_{4}& {x}_{5}& {x}_{6}\\ {x}_{6}& {x}_{7}& {x}_{8}& {x}_{9}& {x}_{10}& {x}_{11}& {x}_{12}& {x}_{1}& {x}_{2}& {x}_{3}& {x}_{4}& {x}_{5}\\ {x}_{5}& {x}_{6}& {x}_{7}& {x}_{8}& {x}_{9}& {x}_{10}& {x}_{11}& {x}_{12}& {x}_{1}& {x}_{2}& {x}_{3}& {x}_{4}\\ {x}_{4}& {x}_{5}& {x}_{6}& {x}_{7}& {x}_{8}& {x}_{9}& {x}_{10}& {x}_{11}& {x}_{12}& {x}_{1}& {x}_{2}& {x}_{3}\\ {x}_{3}& {x}_{4}& {x}_{5}& {x}_{6}& {x}_{7}& {x}_{8}& {x}_{9}& {x}_{10}& {x}_{11}& {x}_{12}& {x}_{1}& {x}_{2}\\ {x}_{2}& {x}_{3}& {x}_{4}& {x}_{5}& {x}_{6}& {x}_{7}& {x}_{8}& {x}_{9}& {x}_{10}& {x}_{11}& {x}_{12}& {x}_{1}\end{array}\right]$ (1.7)
 > $f≔\mathrm{Determinant}\left(A,\mathrm{method}=\mathrm{minor}\right):$
 > $\mathrm{nops}\left(f\right)$
 ${86500}$ (1.8)

This factorization took about 17 seconds in Maple 2018.

 > $F≔\mathrm{CodeTools}:-\mathrm{Usage}\left(\mathrm{factor}\left(f\right)\right):$
 memory used=488.25MiB, alloc change=-41.44MiB, cpu time=5.37s, real time=3.96s, gc time=421.20ms
 > $\mathrm{nops}\left(F\right)$
 ${6}$ (1.9)
 > $\mathrm{map}\left(\mathrm{nops},\left[\mathrm{op}\left(F\right)\right]\right)$
 $\left[{12}{,}{12}{,}{42}{,}{78}{,}{78}{,}{621}\right]$ (1.10)
 > $\mathrm{map}\left(\mathrm{degree},\left[\mathrm{op}\left(F\right)\right]\right)$
 $\left[{1}{,}{1}{,}{2}{,}{2}{,}{2}{,}{4}\right]$ (1.11)
 > $\mathrm{expand}\left(f-F\right)$
 ${0}$ (1.12)

Graph Theory

In Maple 2019 the MaximumClique function of the GraphTheory package has new algorithms for computing the maximum clique of a graph and an option to choose the algorithm that you want to use, giving a huge performance boost on certain kinds of graphs. In the following example, Maple 2019 almost instantly finds the maximum clique of a graph that Maple 2018 needed over 3 minutes to find. In this case the "sat" method is used which translates the problem into Boolean logic and solves the resulting satisfiability problem using a SAT solver.

 > $\mathrm{with}\left(\mathrm{GraphTheory}\right):$
 > $\mathrm{filename}≔\mathrm{FileTools}:-\mathrm{JoinPath}\left(\left[\mathrm{kernelopts}\left(\mathrm{datadir}\right),"example","MANN_a9.clq"\right]\right)$
 ${\mathrm{filename}}{≔}{"E:\Maple2019\data\example\MANN_a9.clq"}$ (2.1)
 >
 ${G}{≔}{\mathrm{Graph 1: an undirected unweighted graph with 45 vertices and 918 edge\left(s\right)}}$ (2.2)
 > $\mathrm{DegreeSequence}\left(G\right)$
 $\left[{40}{,}{40}{,}{40}{,}{40}{,}{40}{,}{40}{,}{40}{,}{40}{,}{40}{,}{41}{,}{41}{,}{41}{,}{41}{,}{41}{,}{41}{,}{41}{,}{41}{,}{41}{,}{41}{,}{41}{,}{41}{,}{41}{,}{41}{,}{41}{,}{41}{,}{41}{,}{41}{,}{41}{,}{41}{,}{41}{,}{41}{,}{41}{,}{41}{,}{41}{,}{41}{,}{41}{,}{41}{,}{41}{,}{41}{,}{41}{,}{41}{,}{41}{,}{41}{,}{41}{,}{41}\right]$ (2.3)
 > $C≔\mathrm{CodeTools}:-\mathrm{Usage}\left(\mathrm{MaximumClique}\left(G,\mathrm{method}='\mathrm{sat}'\right)\right)$
 memory used=10.44MiB, alloc change=28.99MiB, cpu time=187.00ms, real time=152.00ms, gc time=62.40ms
 ${C}{≔}\left[{2}{,}{3}{,}{4}{,}{6}{,}{10}{,}{14}{,}{17}{,}{20}{,}{24}{,}{25}{,}{30}{,}{33}{,}{36}{,}{39}{,}{41}{,}{45}\right]$ (2.4)
 > $\mathrm{numelems}\left(C\right)$
 ${16}$ (2.5)

Group Theory

 • Arithmetic and other low-level operations for permutations have been completely re-written in compiled kernel code. In addition, the memory overhead of permutations has been considerably reduced.
 • For example, the following call to PermOrder took about 200 times longer in Maple 2018.
 > $\mathrm{with}\left(\mathrm{GroupTheory}\right):$
 > $p≔\mathrm{Perm}\left(\mathrm{combinat}:-\mathrm{randperm}\left({10}^{5}\right)\right):$
 > $\mathrm{PermOrder}\left(p\right)$
 ${47396163561937236086040}$ (3.1)
 • Timing details will of course vary from one machine to another, and depend also upon the random state of the Maple session. But, reproduced here are some representative calculations run in a fresh Maple 2018 session,  on a particular 64-bit Linux workstation.
 > $L≔\mathrm{CodeTools}:-\mathrm{Usage}\left(\left[\mathrm{seq}\right]\left(\mathrm{Perm}\left(\mathrm{combinat}:-\mathrm{randperm}\left({10}^{4}\right)\right),i=1..1000\right)\right):$
 > $\mathrm{CodeTools}:-\mathrm{Usage}\left(\mathrm{PermProduct}\left(\mathrm{op}\left(L\right)\right)\right):$
 ${\mathrm{memory used=307.57MiB, alloc change=288.00MiB, cpu time=9.78s, real time=8.36s, gc time=1.75s}}$ (3.2)
 > $\mathrm{CodeTools}:-\mathrm{Usage}\left(\mathrm{map}\left(\mathrm{PermOrder},L\right)\right):$
 ${\mathrm{memory used=2.54GiB, alloc change=96.00MiB, cpu time=52.62s, real time=40.96s, gc time=13.75s}}$ (3.3)
 > $\mathrm{CodeTools}:-\mathrm{Usage}\left(\mathrm{map}\left(\mathrm{PermInverse},L\right)\right):$
 ${\mathrm{memory used=0.74GiB, alloc change=320.00MiB, cpu time=19.56s, real time=14.66s, gc time=5.71s}}$ (3.4)
 > $\mathrm{CodeTools}:-\mathrm{Usage}\left(\mathrm{map}\left(\mathrm{PermCycleType},L\right)\right):$
 ${\mathrm{memory used=0.84MiB, alloc change=0 bytes, cpu time=152.00ms, real time=149.00ms, gc time=0ns}}$ (3.5)
 > $\mathrm{CodeTools}:-\mathrm{Usage}\left(\mathrm{map}\left(\mathrm{PermPower},L,3333\right)\right):$
 ${\mathrm{memory used=4.53GiB, alloc change=2.22GiB, cpu time=3.78m, real time=2.17m, gc time=113.08s}}$ (3.6)
 • And here are the same calculations run in a fresh 2019 session on the same machine. It is apparent that both time used an memory consumption have been considerably reduced.
 > $L≔\mathrm{CodeTools}:-\mathrm{Usage}\left(\left[\mathrm{seq}\right]\left(\mathrm{Perm}\left(\mathrm{combinat}:-\mathrm{randperm}\left({10}^{4}\right)\right),i=1..1000\right)\right):$
 ${\mathrm{memory used=77.16MiB, alloc change=59.42MiB, cpu time=1.10s, real time=1.10s, gc time=8.00ms}}$ (3.7)
 > $\mathrm{CodeTools}:-\mathrm{Usage}\left(\mathrm{PermProduct}\left(\mathrm{op}\left(L\right)\right)\right):$
 ${\mathrm{memory used=77.85MiB, alloc change=0 bytes, cpu time=592.00ms, real time=587.00ms, gc time=24.00ms}}$ (3.8)
 > $\mathrm{CodeTools}:-\mathrm{Usage}\left(\mathrm{map}\left(\mathrm{PermOrder},L\right)\right):$
 ${\mathrm{memory used=8.08MiB, alloc change=3.01MiB, cpu time=204.00ms, real time=203.00ms, gc time=0ns}}$ (3.9)
 > $\mathrm{CodeTools}:-\mathrm{Usage}\left(\mathrm{map}\left(\mathrm{PermInverse},L\right)\right):$
 ${\mathrm{memory used=77.30MiB, alloc change=-1.00MiB, cpu time=568.00ms, real time=560.00ms, gc time=16.00ms}}$ (3.10)
 > $\mathrm{CodeTools}:-\mathrm{Usage}\left(\mathrm{map}\left(\mathrm{PermCycleType},L\right)\right):$
 ${\mathrm{memory used=214.05KiB, alloc change=0 bytes, cpu time=124.00ms, real time=125.00ms, gc time=0ns}}$ (3.11)
 > $\mathrm{CodeTools}:-\mathrm{Usage}\left(\mathrm{map}\left(\mathrm{PermPower},L,3333\right)\right):$
 ${\mathrm{memory used=77.81MiB, alloc change=0 bytes, cpu time=764.00ms, real time=752.00ms, gc time=36.00ms}}$ (3.12)
 Real Root Finding The RootFinding:-Isolate command has a new algorithm for univariate polynomials that is much faster for ill-conditioned problems and high accuracy solutions. See Real Root Finding for details.