$\mathrm{vars}≔\left[\mathrm{seq}\left(x_i\,i=1..8\right)\right]$

$\mathrm{vars}≔\left[x_1\,x_2\,x_3\,x_4\,x_5\,x_6\,x_7\,x_8\right]$

$g≔\mathrm{randpoly}\left(\mathrm{vars}\, \mathrm{degree}\=15\,\mathrm{terms}\=50\,\mathrm{coeffs}\=\mathrm{rand}\left(-1000..1000\right)\right)$

$g≔555x_1^4{x}_2{x}_3^2{x}_5^3{x}_6^2{x}_7{x}_8^2+771x_1^4{x}_2{x}_3{x}_4^2{x}_6^3{x}_8^4+584x_1^3{x}_2{x}_3^4{x}_6{x}_7^6+930x_1^3{x}_4^3{x}_5{x}_6^3{x}_7{x}_8^4-778x_1^2{x}_2^2{x}_3{x}_4{x}_7^8{x}_8-642x_1^2{x}_3^2{x}_4^2{x}_5{x}_6^6{x}_7{x}_8+897x_1^2{x}_4^2{x}_6{x}_7^5{x}_8^5-73x_1{x}_2{x}_3^4{x}_4{x}_6^5{x}_7{x}_8^2+396x_1{x}_2{x}_6^{11}{x}_8^2+728x_2^6{x}_4^3{x}_5^2{x}_6{x}_8^3-981x_2^5{x}_3{x}_4^4{x}_7{x}_8^4-45x_2^3{x}_3{x}_4^4{x}_5^5{x}_7{x}_8-173x_2^2{x}_3{x}_4^3{x}_6^6{x}_7{x}_8^2+369x_2^2{x}_5^3{x}_6^4{x}_7^5{x}_8+190x_2{x}_4^5{x}_5^3{x}_7{x}_8^5-257x_3^9{x}_5^2{x}_6^3{x}_7+227x_3^2{x}_4^7{x}_7^4{x}_8^2+83x_3{x}_4{x}_6^{11}{x}_8^2+809x_5^3{x}_6{x}_7^2{x}_8^9-921x_1^6{x}_2^3{x}_4^5-466x_1^2{x}_2^2{x}_3^4{x}_6{x}_8^5-265x_1^2{x}_2^2{x}_5^2{x}_6^5{x}_7^2{x}_8-394x_1{x}_2{x}_3^2{x}_4^3{x}_5^2{x}_6^4{x}_7+898x_1{x}_3^5{x}_6^4{x}_7^2{x}_8^2-916x_1{x}_4{x}_6^8{x}_7^3{x}_8-583x_2^3{x}_4{x}_5^8{x}_7^2-932x_3^4{x}_7^{10}-588x_4^4{x}_6^7{x}_7^2{x}_8+989x_4^3{x}_5^6{x}_6^2{x}_7^2{x}_8+330x_1^2{x}_2^3{x}_4{x}_5^2{x}_6^3{x}_8^2+510x_1^2{x}_2^2{x}_4^2{x}_6^2{x}_8^5+587x_1^2{x}_5^2{x}_7^7{x}_8^2+430x_1{x}_2^2{x}_4^6{x}_5{x}_6{x}_7^2+67x_2^2{x}_3^3{x}_4^3{x}_5{x}_8^4-296x_1^3{x}_2^6{x}_3{x}_4{x}_7-799x_1^3{x}_2{x}_3{x}_5^3{x}_7^3{x}_8+717x_1^2{x}_2^5{x}_4{x}_6^2{x}_8^2+550x_1^2{x}_2{x}_5^2{x}_7{x}_8^6-417x_1^2{x}_3^2{x}_4{x}_5^4{x}_6{x}_8^2-991x_2^7{x}_3{x}_4{x}_5^2{x}_6-672x_2^2{x}_3^2{x}_4{x}_6^5{x}_7^2-434x_2^2{x}_4^2{x}_5{x}_7^6{x}_8+399x_2^2{x}_4{x}_5^5{x}_6{x}_7{x}_8^2-23x_2{x}_3^6{x}_4^2{x}_6{x}_7{x}_8-500x_1^5{x}_3^3{x}_4{x}_5^2-630x_1{x}_2{x}_3{x}_4^6{x}_6{x}_7-513x_1{x}_2{x}_3{x}_4{x}_5^4{x}_7{x}_8^2+322x_2{x}_4^3{x}_5^2{x}_7^4{x}_8-933x_3{x}_4^4{x}_5^3{x}_8+545x_5^2{x}_6{x}_7^5$

$h≔\mathrm{randpoly}\left(\mathrm{vars}\, \mathrm{degree}\=15\,\mathrm{terms}\=50\,\mathrm{coeffs}\=\mathrm{rand}\left(-1000..1000\right)\right)$

$h≔-474x_1^5{x}_3^4{x}_4^3{x}_5{x}_6^2+429x_1^4{x}_2^2{x}_3{x}_6^4{x}_7^3{x}_8-188x_1^3{x}_2{x}_3^2{x}_4^3{x}_6^3{x}_7^2{x}_8-197x_1^3{x}_2{x}_3{x}_4{x}_5^3{x}_6^3{x}_7{x}_8^2-464x_1^2{x}_2{x}_3^3{x}_4^3{x}_6{x}_7^4{x}_8-495x_1^2{x}_3^4{x}_5{x}_6^2{x}_7^6+725x_1{x}_2^6{x}_5^4{x}_7^4+811x_1{x}_2^3{x}_3{x}_4^4{x}_5^4{x}_6{x}_7-26x_1{x}_2{x}_3^3{x}_4^4{x}_5^2{x}_6{x}_7^3+470x_2^3{x}_5^7{x}_7^3{x}_8^2+159x_2{x}_3^4{x}_5^4{x}_8^6-631x_1^5{x}_2^3{x}_3{x}_4^4{x}_7-910x_1^4{x}_4^3{x}_6{x}_7^4{x}_8^2+527x_1^3{x}_2{x}_3^5{x}_5^2{x}_8^3+558x_1^3{x}_2{x}_3^3{x}_4^5{x}_7^2-168x_1^3{x}_4^4{x}_6^3{x}_8^4+920x_1^2{x}_2^6{x}_4^2{x}_7^3{x}_8-672x_1{x}_2^4{x}_4^3{x}_6^5{x}_8+201x_1{x}_2^2{x}_4^9{x}_6{x}_8+660x_1{x}_2{x}_5^6{x}_6^5{x}_7+153x_1{x}_5^8{x}_7^2{x}_8^3-628x_2^6{x}_3{x}_4^3{x}_5^3{x}_8+771x_2^3{x}_4^2{x}_5^9-710x_2^2{x}_4^6{x}_5^2{x}_7^4+392x_2^2{x}_5^7{x}_8^5+211x_2{x}_4^6{x}_5{x}_6^3{x}_8^3-997x_3^3{x}_4{x}_5^5{x}_6^2{x}_7{x}_8^2-968x_3{x}_5{x}_7^{12}-160x_1^4{x}_2^2{x}_5^2{x}_8^5-488x_1^3{x}_3{x}_5^2{x}_7^7+554x_1^2{x}_2^2{x}_3^3{x}_4^6-687x_1^2{x}_2{x}_4^2{x}_5{x}_6^3{x}_7^2{x}_8^2+665x_1{x}_2^3{x}_3^3{x}_4^3{x}_8^3+870x_2^2{x}_3^6{x}_5^3{x}_7{x}_8-160x_2^2{x}_5^4{x}_7^7+136x_2{x}_3^2{x}_4^2{x}_6{x}_7^6{x}_8-487x_1^4{x}_2{x}_3^5{x}_5{x}_8+549x_1{x}_2^3{x}_3^2{x}_4^3{x}_5{x}_6^2-262x_1{x}_2^2{x}_6^4{x}_7{x}_8^4+649x_1{x}_2{x}_3^2{x}_4^4{x}_6^2{x}_8^2+864x_1{x}_2{x}_3^2{x}_4^2{x}_6^3{x}_7{x}_8^2+336x_1^3{x}_2{x}_3^2{x}_4^2{x}_6{x}_7{x}_8-679x_1{x}_2{x}_3^3{x}_4{x}_5^3{x}_7{x}_8+871x_2^2{x}_3^7{x}_4{x}_7-823x_3^3{x}_4^6{x}_6{x}_8+386x_1{x}_2^2{x}_6^3{x}_7{x}_8^3-373x_2{x}_5^4{x}_6^3{x}_8+511x_1^2{x}_2{x}_4{x}_7^2{x}_8^2-838x_2^2{x}_6{x}_7^4{x}_8-124x_2^3{x}_4{x}_5{x}_7$

$f≔\mathrm{expand}\left(g\cdot h\right)\:$

$\mathrm{CodeTools}:-\mathrm{Usage}\left(\mathrm{factor}\left(f\right)\right)$

memory used=40.03MiB, alloc change=41.09MiB, cpu time=250.00ms, real time=247.00ms, gc time=0ns

$\left(474x_1^5{x}_3^4{x}_4^3{x}_5{x}_6^2-429x_1^4{x}_2^2{x}_3{x}_6^4{x}_7^3{x}_8+188x_1^3{x}_2{x}_3^2{x}_4^3{x}_6^3{x}_7^2{x}_8+197x_1^3{x}_2{x}_3{x}_4{x}_5^3{x}_6^3{x}_7{x}_8^2+464x_1^2{x}_2{x}_3^3{x}_4^3{x}_6{x}_7^4{x}_8+495x_1^2{x}_3^4{x}_5{x}_6^2{x}_7^6-725x_1{x}_2^6{x}_5^4{x}_7^4-811x_1{x}_2^3{x}_3{x}_4^4{x}_5^4{x}_6{x}_7+26x_1{x}_2{x}_3^3{x}_4^4{x}_5^2{x}_6{x}_7^3-470x_2^3{x}_5^7{x}_7^3{x}_8^2-159x_2{x}_3^4{x}_5^4{x}_8^6+631x_1^5{x}_2^3{x}_3{x}_4^4{x}_7+910x_1^4{x}_4^3{x}_6{x}_7^4{x}_8^2-527x_1^3{x}_2{x}_3^5{x}_5^2{x}_8^3-558x_1^3{x}_2{x}_3^3{x}_4^5{x}_7^2+168x_1^3{x}_4^4{x}_6^3{x}_8^4-920x_1^2{x}_2^6{x}_4^2{x}_7^3{x}_8+672x_1{x}_2^4{x}_4^3{x}_6^5{x}_8-201x_1{x}_2^2{x}_4^9{x}_6{x}_8-660x_1{x}_2{x}_5^6{x}_6^5{x}_7-153x_1{x}_5^8{x}_7^2{x}_8^3+628x_2^6{x}_3{x}_4^3{x}_5^3{x}_8-771x_2^3{x}_4^2{x}_5^9+710x_2^2{x}_4^6{x}_5^2{x}_7^4-392x_2^2{x}_5^7{x}_8^5-211x_2{x}_4^6{x}_5{x}_6^3{x}_8^3+997x_3^3{x}_4{x}_5^5{x}_6^2{x}_7{x}_8^2+968x_3{x}_5{x}_7^{12}+160x_1^4{x}_2^2{x}_5^2{x}_8^5+488x_1^3{x}_3{x}_5^2{x}_7^7-554x_1^2{x}_2^2{x}_3^3{x}_4^6+687x_1^2{x}_2{x}_4^2{x}_5{x}_6^3{x}_7^2{x}_8^2-665x_1{x}_2^3{x}_3^3{x}_4^3{x}_8^3-870x_2^2{x}_3^6{x}_5^3{x}_7{x}_8+160x_2^2{x}_5^4{x}_7^7-136x_2{x}_3^2{x}_4^2{x}_6{x}_7^6{x}_8+487x_1^4{x}_2{x}_3^5{x}_5{x}_8-549x_1{x}_2^3{x}_3^2{x}_4^3{x}_5{x}_6^2+262x_1{x}_2^2{x}_6^4{x}_7{x}_8^4-649x_1{x}_2{x}_3^2{x}_4^4{x}_6^2{x}_8^2-864x_1{x}_2{x}_3^2{x}_4^2{x}_6^3{x}_7{x}_8^2-336x_1^3{x}_2{x}_3^2{x}_4^2{x}_6{x}_7{x}_8+679x_1{x}_2{x}_3^3{x}_4{x}_5^3{x}_7{x}_8-871x_2^2{x}_3^7{x}_4{x}_7+823x_3^3{x}_4^6{x}_6{x}_8-386x_1{x}_2^2{x}_6^3{x}_7{x}_8^3+373x_2{x}_5^4{x}_6^3{x}_8-511x_1^2{x}_2{x}_4{x}_7^2{x}_8^2+838x_2^2{x}_6{x}_7^4{x}_8+124x_2^3{x}_4{x}_5{x}_7\right)\left(-555x_1^4{x}_2{x}_3^2{x}_5^3{x}_6^2{x}_7{x}_8^2-771x_1^4{x}_2{x}_3{x}_4^2{x}_6^3{x}_8^4-584x_1^3{x}_2{x}_3^4{x}_6{x}_7^6-930x_1^3{x}_4^3{x}_5{x}_6^3{x}_7{x}_8^4+778x_1^2{x}_2^2{x}_3{x}_4{x}_7^8{x}_8+642x_1^2{x}_3^2{x}_4^2{x}_5{x}_6^6{x}_7{x}_8-897x_1^2{x}_4^2{x}_6{x}_7^5{x}_8^5+73x_1{x}_2{x}_3^4{x}_4{x}_6^5{x}_7{x}_8^2-396x_1{x}_2{x}_6^{11}{x}_8^2-728x_2^6{x}_4^3{x}_5^2{x}_6{x}_8^3+981x_2^5{x}_3{x}_4^4{x}_7{x}_8^4+45x_2^3{x}_3{x}_4^4{x}_5^5{x}_7{x}_8+173x_2^2{x}_3{x}_4^3{x}_6^6{x}_7{x}_8^2-369x_2^2{x}_5^3{x}_6^4{x}_7^5{x}_8-190x_2{x}_4^5{x}_5^3{x}_7{x}_8^5+257x_3^9{x}_5^2{x}_6^3{x}_7-227x_3^2{x}_4^7{x}_7^4{x}_8^2-83x_3{x}_4{x}_6^{11}{x}_8^2-809x_5^3{x}_6{x}_7^2{x}_8^9+921x_1^6{x}_2^3{x}_4^5+466x_1^2{x}_2^2{x}_3^4{x}_6{x}_8^5+265x_1^2{x}_2^2{x}_5^2{x}_6^5{x}_7^2{x}_8+394x_1{x}_2{x}_3^2{x}_4^3{x}_5^2{x}_6^4{x}_7-898x_1{x}_3^5{x}_6^4{x}_7^2{x}_8^2+916x_1{x}_4{x}_6^8{x}_7^3{x}_8+583x_2^3{x}_4{x}_5^8{x}_7^2+932x_3^4{x}_7^{10}+588x_4^4{x}_6^7{x}_7^2{x}_8-989x_4^3{x}_5^6{x}_6^2{x}_7^2{x}_8-330x_1^2{x}_2^3{x}_4{x}_5^2{x}_6^3{x}_8^2-510x_1^2{x}_2^2{x}_4^2{x}_6^2{x}_8^5-587x_1^2{x}_5^2{x}_7^7{x}_8^2-430x_1{x}_2^2{x}_4^6{x}_5{x}_6{x}_7^2-67x_2^2{x}_3^3{x}_4^3{x}_5{x}_8^4+296x_1^3{x}_2^6{x}_3{x}_4{x}_7+799x_1^3{x}_2{x}_3{x}_5^3{x}_7^3{x}_8-717x_1^2{x}_2^5{x}_4{x}_6^2{x}_8^2-550x_1^2{x}_2{x}_5^2{x}_7{x}_8^6+417x_1^2{x}_3^2{x}_4{x}_5^4{x}_6{x}_8^2+991x_2^7{x}_3{x}_4{x}_5^2{x}_6+672x_2^2{x}_3^2{x}_4{x}_6^5{x}_7^2+434x_2^2{x}_4^2{x}_5{x}_7^6{x}_8-399x_2^2{x}_4{x}_5^5{x}_6{x}_7{x}_8^2+23x_2{x}_3^6{x}_4^2{x}_6{x}_7{x}_8+500x_1^5{x}_3^3{x}_4{x}_5^2+630x_1{x}_2{x}_3{x}_4^6{x}_6{x}_7+513x_1{x}_2{x}_3{x}_4{x}_5^4{x}_7{x}_8^2-322x_2{x}_4^3{x}_5^2{x}_7^4{x}_8+933x_3{x}_4^4{x}_5^3{x}_8-545x_5^2{x}_6{x}_7^5\right)$

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

$\mathrm{nops}\left(f\right)$

$29791$

$F≔\mathrm{CodeTools}:-\mathrm{Usage}\left(\mathrm{factor}\left(f\right)\right)\:$

memory used=475.20MiB, alloc change=133.50MiB, cpu time=3.29s, real time=3.08s, gc time=468.00ms

$\mathrm{nops}\left(F\right)$

$3$

$\mathrm{with}\left(\mathrm{LinearAlgebra}\right)\: \mathrm{interface}\left(\mathrm{rtablesize}\=12\right)\:$

$A≔\mathrm{Matrix}\left(12\,\mathrm{shape}\=\mathrm{Circulant}\left[\left[\mathrm{seq}\left(x_j\,j\=1..12\right)\right]\right]\right)$

$A≔\left[\begin{array}{cccccccccccc}{x}_1& x_2& x_3& x_4& x_5& x_6& x_7& x_8& x_9& x_{10}& x_{11}& x_{12}\\ x_{12}& x_1& x_2& x_3& x_4& x_5& x_6& x_7& x_8& x_9& x_{10}& x_{11}\\ x_{11}& x_{12}& x_1& x_2& x_3& x_4& x_5& x_6& x_7& x_8& x_9& x_{10}\\ x_{10}& x_{11}& x_{12}& x_1& x_2& x_3& x_4& x_5& x_6& x_7& x_8& x_9\\ x_9& x_{10}& x_{11}& x_{12}& x_1& x_2& x_3& x_4& x_5& x_6& x_7& x_8\\ x_8& x_9& x_{10}& x_{11}& x_{12}& x_1& x_2& x_3& x_4& x_5& x_6& x_7\\ x_7& x_8& x_9& x_{10}& x_{11}& x_{12}& x_1& x_2& x_3& x_4& x_5& x_6\\ x_6& x_7& x_8& x_9& x_{10}& x_{11}& x_{12}& x_1& x_2& x_3& x_4& x_5\\ x_5& x_6& x_7& x_8& x_9& x_{10}& x_{11}& x_{12}& x_1& x_2& x_3& x_4\\ x_4& x_5& x_6& x_7& x_8& x_9& x_{10}& x_{11}& x_{12}& x_1& x_2& x_3\\ x_3& x_4& x_5& x_6& x_7& x_8& x_9& x_{10}& x_{11}& x_{12}& x_1& x_2\\ x_2& x_3& x_4& x_5& x_6& x_7& x_8& x_9& x_{10}& x_{11}& x_{12}& x_1\end{array}\right]$

$f≔\mathrm{Determinant}\left(A\,\mathrm{method}\=\mathrm{minor}\right)\:$

$\mathrm{nops}\left(f\right)$

$86500$

$F≔\mathrm{CodeTools}:-\mathrm{Usage}\left(\mathrm{factor}\left(f\right)\right)\:$

memory used=488.25MiB, alloc change=-41.44MiB, cpu time=5.37s, real time=3.96s, gc time=421.20ms

$\mathrm{nops}\left(F\right)$

$6$

$\mathrm{map}\left(\mathrm{nops}\,\left[\mathrm{op}\left(F\right)\right]\right)$

$\left[12\,12\,42\,78\,78\,621\right]$

$\mathrm{map}\left(\mathrm{degree}\,\left[\mathrm{op}\left(F\right)\right]\right)$

$\left[1\,1\,2\,2\,2\,4\right]$

$\mathrm{expand}\left(f-F\right)$

$0$

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

$\mathrm{filename}≔\mathrm{FileTools}:-\mathrm{JoinPath}\left(\left[\mathrm{kernelopts}\left(\mathrm{datadir}\right)\,''example''\,''MANN\_a9.clq''\right]\right)$

$\mathrm{filename}≔''E:\backslash Maple2019\backslash data\backslash example\backslash MANN\_a9.clq''$

$G≔\mathrm{ImportGraph}\left(\mathrm{filename}\, \'\mathrm{dimacs}\'\right)$

$G≔\mathrm{Graph\; 1:\; an\; undirected\; unweighted\; graph\; with\; 45\; vertices\; and\; 918\; edge(s)}$

$\mathrm{DegreeSequence}\left(G\right)$

$\left[40\,40\,40\,40\,40\,40\,40\,40\,40\,41\,41\,41\,41\,41\,41\,41\,41\,41\,41\,41\,41\,41\,41\,41\,41\,41\,41\,41\,41\,41\,41\,41\,41\,41\,41\,41\,41\,41\,41\,41\,41\,41\,41\,41\,41\right]$

$C≔\mathrm{CodeTools}:-\mathrm{Usage}\left(\mathrm{MaximumClique}\left(G\,\mathrm{method}\=\'\mathrm{sat}\'\right)\right)$

memory used=10.44MiB, alloc change=28.99MiB, cpu time=187.00ms, real time=152.00ms, gc time=62.40ms

$C≔\left[2\,3\,4\,6\,10\,14\,17\,20\,24\,25\,30\,33\,36\,39\,41\,45\right]$

$\mathrm{numelems}\left(C\right)$

$16$

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.

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

$p≔\mathrm{Perm}\left(\mathrm{combinat}:-\mathrm{randperm}\left({10}^5\right)\right)\:$

$\mathrm{PermOrder}\left(p\right)$

$47396163561937236086040$

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.

$L≔\mathrm{CodeTools}:-\mathrm{Usage}\left(\left[\mathrm{seq}\right]\left(\mathrm{Perm}\left(\mathrm{combinat}:-\mathrm{randperm}\left({10}^4\right)\right)\,i=1..1000\right)\right)\:$

$\mathrm{CodeTools}:-\mathrm{Usage}\left(\mathrm{PermProduct}\left(\mathrm{op}\left(L\right)\right)\right)\:$

$\mathrm{memory\; used=307.57MiB,\; alloc\; change=288.00MiB,\; cpu\; time=9.78s,\; real\; time=8.36s,\; gc\; time=1.75s}$

$\mathrm{CodeTools}:-\mathrm{Usage}\left(\mathrm{map}\left(\mathrm{PermOrder}\,L\right)\right)\:$

$\mathrm{memory\; used=2.54GiB,\; alloc\; change=96.00MiB,\; cpu\; time=52.62s,\; real\; time=40.96s,\; gc\; time=13.75s}$

$\mathrm{CodeTools}:-\mathrm{Usage}\left(\mathrm{map}\left(\mathrm{PermInverse}\,L\right)\right)\:$