diff --git a/changelog b/changelog index 6ac2d76..a888ba0 100644 --- a/changelog +++ b/changelog @@ -1,3 +1,5 @@ +20140630 tpd src/axiom-website/patches.html 20140630.01.tpd.patch +20140630 tpd src/input/wangeez.input Paul Wang's EEZ test polynmials 20140629 tpd src/axiom-website/patches.html 20140629.06.tpd.patch 20140629 tpd books/tangle.c improve the debugging output (DEBUG==3) 20140629 tpd src/axiom-website/patches.html 20140629.05.tpd.patch diff --git a/patch b/patch index 40f2fed..64b8a48 100644 --- a/patch +++ b/patch @@ -1,6 +1,5 @@ -books/tangle.c improve the debugging output (DEBUG==3) - -Improve the debugging output (DEBUG==3) so that it is obvious -what chunk is being expanded. It also shows the expanded output -delimited by begin/end markers. +src/input/wangeez.input Paul Wang's EEZ test polynmials +These are the test polynomials for the EEZ polynomial factorization +algorithm proposed by Paul Wang in his paper ``An Improved Multivariate +Polynomial Factoring Algorithm'' \cite{Wang78} diff --git a/src/axiom-website/patches.html b/src/axiom-website/patches.html index d1a1461..cc0e387 100644 --- a/src/axiom-website/patches.html +++ b/src/axiom-website/patches.html @@ -4514,6 +4514,8 @@ Makefile default to notests for users books/bookvol10.3 add information to SingleInteger 20140629.06.tpd.patch books/tangle.c improve the debugging output (DEBUG==3) +20140630.01.tpd.patch +src/input/wangeez.input Paul Wang's EEZ test polynmials diff --git a/src/input/Makefile.pamphlet b/src/input/Makefile.pamphlet index 3229552..a879c5f 100644 --- a/src/input/Makefile.pamphlet +++ b/src/input/Makefile.pamphlet @@ -414,7 +414,8 @@ REGRESSTESTS= ackermann.regress \ triglim.regress tsetcatvermeer.regress tutchap1.regress \ typetower.regress void.regress uniseg.regress \ unittest1.regress unittest2.regress unittest3.regress unittest4.regress \ - unit-macro.regress zimmbron.regress zimmer.regress + unit-macro.regress wangeez.regress \ + zimmbron.regress zimmer.regress \end{chunk} \begin{chunk}{regression tests} @@ -936,7 +937,8 @@ FILES= ${OUT}/ackermann.input \ ${OUT}/vector.input ${OUT}/vectors.input ${OUT}/viewdef.input \ ${OUT}/void.input ${OUT}/wiggle.input \ ${OUT}/wutset.input \ - ${OUT}/xpoly.input ${OUT}/xpr.input ${OUT}/zimmbron.input \ + ${OUT}/xpoly.input ${OUT}/xpr.input ${OUT}/wangeez.input \ + ${OUT}/zimmbron.input \ ${OUT}/zdsolve.input ${OUT}/zimmer.input ${OUT}/zlindep.input FILES2=${OUT}/arith.input ${OUT}/bugs.input \ @@ -1461,7 +1463,7 @@ DOCFILES= \ ${DOC}/wester.input.dvi ${DOC}/wiggle.input.dvi \ ${DOC}/wutset.input.dvi \ ${DOC}/xpoly.input.dvi ${DOC}/xpr.input.dvi \ - ${DOC}/zimmbron.input.dvi \ + ${DOC}/wangeez.input.dvi ${DOC}/zimmbron.input.dvi \ ${DOC}/zdsolve.input.dvi ${DOC}/zimmer.input.dvi \ ${DOC}/zlindep.input.dvi diff --git a/src/input/wangeez.input.pamphlet b/src/input/wangeez.input.pamphlet new file mode 100644 index 0000000..3f37c43 --- /dev/null +++ b/src/input/wangeez.input.pamphlet @@ -0,0 +1,1171 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input wangeez.input} +\author{Paul Wang and Timothy Daly} +\maketitle +\begin{abstract} +These are the test polynomials for the EEZ polynomial factorization +algorithm proposed by Paul Wang in his paper ``An Improved Multivariate +Polynomial Factoring Algorithm'' \cite{Wang78} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f wangeez.output +)spool wangeez.output +)set message test on +)set message auto off +)clear all + +--S 1 of 45 +t1:=(z + xy + 10)*(xz + y + 30)*(yz + x + 20) +--R +--R +--R (1) +--R ((y + xz + 30)yz + (x + 20)y + (x + 20)xz + 30x + 600)z +--R + +--R ((xy + 10)y + (xy + 10)xz + 30xy + 300)yz + ((x + 20)xy + 10x + 200)y +--R + +--R ((x + 20)xy + 10x + 200)xz + (30x + 600)xy + 300x + 6000 +--R Type: Polynomial(Integer) +--E 1 + +--S 2 of 45 +t1f:=factor t1 +--R +--R +--R (2) (y + xz + 30)(yz + x + 20)(z + xy + 10) +--R Type: Factored(Polynomial(Integer)) +--E 2 + +--S 3 of 45 +t1-t1f +--R +--R +--R (3) 0 +--R Type: Factored(Polynomial(Integer)) +--E 3 + +--S 4 of 45 +t2:=(x^3*(z + y) + z - 11)*(x^2*(z^2 + y^2) + y + 90) +--R +--R +--R (4) +--R 5 2 3 5 2 2 5 2 2 3 3 +--R (x + x )z + (x y - 11x )z + ((x + x )y + (x + 1)y + 90x + 90)z +--R + +--R 5 3 3 2 2 3 +--R x y + (x - 11x )y + (90x - 11)y - 990 +--R Type: Polynomial(Integer) +--E 4 + +--S 5 of 45 +t2f:=factor t2 +--R +--R +--R 3 3 2 2 2 2 +--R (5) ((x + 1)z + x y - 11)(x z + x y + y + 90) +--R Type: Factored(Polynomial(Integer)) +--E 5 + +--S 6 of 45 +t2-t2f +--R +--R +--R (6) 0 +--R Type: Factored(Polynomial(Integer)) +--E 6 + +--S 7 of 45 +t3:=(y*z^3 + xyz + y^2 + x^3)*(x*(z^4 + 1) + z + x^3*y^2) +--R +--R +--R (7) +--R 7 2 4 4 3 3 3 2 3 +--R x y z + (x y + y + x xyz + x )z + (x y + x y)z + (y + xyz + x )z +--R + +--R 3 4 3 6 2 4 +--R x y + (x xyz + x + x)y + x xyz + x +--R Type: Polynomial(Integer) +--E 7 + +--S 8 of 45 +t3f:=factor t3 +--R +--R +--R 3 2 3 4 3 2 +--R (8) (y z + y + xyz + x )(x z + z + x y + x) +--R Type: Factored(Polynomial(Integer)) +--E 8 + +--S 9 of 45 +t3-t3f +--R +--R +--R (9) 0 +--R Type: Factored(Polynomial(Integer)) +--E 9 + +--S 10 of 45 +t4:=(z^2 - x^3*y + 3)*(z^2 + x*y^3)*(z^2 + x^3*y^4)*(y^4*z^2 + x^2*z + 5) +--R +--R +--R (10) +--R 4 8 2 7 3 8 7 3 5 4 6 +--R y z + x z + (x y + x y - x y + 3y + 5)z +--R + +--R 5 4 3 3 5 2 5 +--R (x y + x y - x y + 3x )z +--R + +--R 4 11 6 9 4 3 8 7 3 4 3 3 4 +--R (x y - x y + (- x + 3x )y + 3x y + 5x y + 5x y - 5x y + 15)z +--R + +--R 6 7 8 5 6 5 4 3 3 3 +--R (x y - x y + (- x + 3x )y + 3x y )z +--R + +--R 7 12 4 11 4 7 6 5 4 3 4 3 2 +--R (- x y + 3x y + 5x y - 5x y + (- 5x + 15x )y + 15x y )z +--R + +--R 9 8 6 7 7 8 4 7 +--R (- x y + 3x y )z - 5x y + 15x y +--R Type: Polynomial(Integer) +--E 10 + +--S 11 of 45 +t4f:=factor t4 +--R +--R +--R 2 3 2 3 2 3 4 4 2 2 +--R (11) (z - x y + 3)(z + x y )(z + x y )(y z + x z + 5) +--R Type: Factored(Polynomial(Integer)) +--E 11 + +--S 12 of 45 +t4-t4f +--R +--R +--R (12) 0 +--R Type: Factored(Polynomial(Integer)) +--E 12 + +--S 13 of 45 +t5:=(z^2 + x^3*y^4 + u^2)*((y^2 + x)*z^2 + 3*u^2*x^3*y^4*z + 19*y^2)*_ + (u^2*y^4*z^2 + x^2*z + 5)*(w^4*z^3 - x*y^2*z^2 - w^4*x^5*y^6 - w^2*x^3*y)*_ + (-x^5*z^3 + y*z + x^2*y^3) +--R +--R +--R (13) +--R 2 4 5 6 2 4 6 4 12 +--R (- u w x y - u w x y )z +--R + +--R 4 4 8 2 6 8 2 7 6 4 7 2 4 8 11 +--R ((- 3u w x + u x )y + u x y - w x y - w x )z +--R + +--R 4 9 2 4 8 10 2 4 9 8 2 4 7 4 2 4 5 6 +--R (3u x - u w x )y - u w x y + u w y + (- u - 19u )w x y +--R + +--R 2 4 5 2 4 10 8 4 4 6 4 9 4 5 2 4 6 +--R u w x y + (- 3u w x + x - u w x )y + (x - 5w x )y - 5w x +--R * +--R 10 +--R z +--R + +--R 4 4 11 2 4 10 2 9 12 2 4 11 2 10 10 +--R (- 3u w x + u w x + u x )y + (u w x + u x )y +--R + +--R 4 4 3 2 4 2 2 9 6 4 8 4 2 6 8 +--R (3u w x + u w x - u x)y + (- 3u w x + (u + 19u )x )y +--R + +--R 2 2 8 2 4 3 2 2 7 2 11 4 10 4 7 6 2 2 9 5 +--R (u w x + u w x - u x )y + (3u x - w x + u x )y + u w x y +--R + +--R 4 11 2 4 8 6 4 4 2 3 2 4 7 2 4 3 +--R (- w x - 15u w x + 5x )y + w x y + ((- u - 19)w + 5)x y + w x y +--R + +--R 2 4 8 +--R - u w x +--R * +--R 9 +--R z +--R + +--R 4 4 13 4 12 14 4 4 5 4 4 2 4 2 3 11 +--R (3u w x + 3u x )y + (3u w x - 3u x + (u w - u )x )y +--R + +--R 6 9 2 4 8 10 4 2 11 2 4 2 4 9 +--R (3u x - 19u w x )y + (3u w x + (u w - u )x )y +--R + +--R 2 4 13 4 12 11 8 4 2 4 7 +--R (- 3u w x + w x + x )y + (u + 19u )w y +--R + +--R 4 13 12 2 9 4 8 4 4 5 6 +--R (w x + x + 15u x - 5w x - 19u w x )y +--R + +--R 2 4 5 4 4 3 4 4 5 4 4 10 4 9 2 8 4 +--R (3u w x + w x - x + u w x)y + (- 3u w x - 5w x + (u + 19)x )y +--R + +--R 2 10 4 5 4 4 3 2 9 2 4 5 2 +--R (w x + w x - x + 5w )y + (u x + (- 5u - 95)w x )y +--R + +--R 2 11 4 2 4 6 +--R (w x + 5w x)y - 5u w x +--R * +--R 8 +--R z +--R + +--R 2 4 13 16 2 4 14 14 4 4 4 6 2 4 13 +--R u w x y + u w x y + ((3u w - 3u )x - u x )y +--R + +--R 4 2 4 10 2 9 12 2 2 11 2 5 11 +--R ((u + 19u )w x + 19u x )y + (u w x - u x )y +--R + +--R 2 4 15 2 14 4 4 11 10 +--R (3u w x + 3u x + u w x )y +--R + +--R 2 2 12 6 4 3 4 2 4 2 4 2 9 +--R (u w x + 3u w x + (u + 19u )w x + (- u - 19u )x)y +--R + +--R 2 4 11 4 10 9 4 6 2 2 3 8 +--R (- 15u w x + 5w x + 5x + 19u x - u w x )y +--R + +--R 4 2 2 8 2 4 7 2 6 4 5 4 4 3 4 2 7 +--R ((u + 19u )w x + 3u w x - 3u x + (w - 1)x + u w x - u x )y +--R + +--R 4 4 11 4 10 2 2 4 6 +--R ((5w + 3u )x + (- 19w + 5)x - u w x )y +--R + +--R 2 2 13 4 2 9 4 6 2 4 3 4 2 5 +--R (3u w x + u w x + (w - 1)x + 15u w x + 5w x - 5x)y +--R + +--R 4 4 8 2 6 4 2 8 4 3 2 4 2 3 +--R (- 15u w x + (5u + 95)x )y + (5w x + 5w x + ((u + 19)w - 5)x )y +--R + +--R 2 4 2 7 2 2 9 2 4 3 +--R (- 19u w + 5u )x y + (5w x + u w x )y +--R * +--R 7 +--R z +--R + +--R 4 4 16 18 2 4 4 7 2 6 15 6 4 13 14 +--R 3u w x y + ((- u w - 3u )x - u x )y + 3u w x y +--R + +--R 4 2 14 2 4 8 2 7 13 4 15 12 +--R (3u w x - u w x - u x )y + w x y +--R + +--R 6 4 5 6 4 2 4 4 2 3 11 +--R (3u w x - 3u x + (19u w - u - 19u )x )y +--R + +--R 4 16 2 4 13 2 12 4 2 6 2 2 5 10 +--R (w x + 15u w x + 15u x - 3u w x - u w x )y +--R + +--R 6 2 11 2 4 2 8 6 4 4 9 +--R (3u w x + (3u w - 3u )x - x - u x )y +--R + +--R 2 4 12 11 2 2 6 8 +--R ((u + 19)w x + 19x - u w x )y +--R + +--R 2 13 7 2 4 5 2 4 4 3 4 4 7 +--R (w x - x + 15u w x - 15u x + (5w - 5)x + 19u w )y +--R + +--R 2 4 13 4 9 4 8 6 +--R (u w x + 15u x - 95w x )y +--R + +--R 2 14 2 2 11 4 4 5 2 4 4 2 3 5 +--R (w x + 15u w x + 3u w x + ((u + 24)w - 5)x + (- u - 19)x )y +--R + +--R 2 8 2 5 4 2 2 10 2 4 5 2 4 2 4 3 +--R (19u x - w x )y + ((u + 19)w x + u w x - u x + (5u + 95)w )y +--R + +--R 2 6 2 4 5 2 2 2 11 2 4 +--R (- w x - 95u w x )y + (u w x + 5u w x)y +--R * +--R 6 +--R z +--R + +--R 4 4 10 4 9 2 4 8 17 2 4 13 16 2 4 9 15 +--R (- 3u w x - 3u x - u w x )y + 19u w x y - u w x y +--R + +--R 2 4 18 14 6 6 4 4 5 2 4 13 +--R 3u w x y + (- 3u x - u w x - 19u x )y +--R + +--R 4 13 4 4 10 4 2 8 2 2 6 12 +--R (5w x + 19u w x - 3u w x - u w x )y +--R + +--R 2 2 11 4 2 9 8 4 4 6 11 +--R (19u w x + (- w - 3u )x - x - u w x )y +--R + +--R 4 4 15 4 14 2 2 7 10 +--R (3u w x + 5w x - u w x )y +--R + +--R 2 2 16 4 10 9 2 4 2 6 4 4 4 2 4 9 +--R (3u w x - w x - x + (15u w - 15u )x - 5x + 19u w x - 19u x)y +--R + +--R 2 4 10 9 4 2 2 3 8 +--R ((5u + 95)w x + 95x + (- u - 19u )w x )y +--R + +--R 2 11 4 2 8 4 4 7 4 6 4 2 5 7 +--R (5w x + 19u w x + 3u w x - 3u x + (19w - u - 24)x )y +--R + +--R 2 4 11 2 2 8 2 7 4 2 4 6 +--R (5u w x - 3u w x - w x - u w x )y +--R + +--R 4 2 13 2 12 2 6 4 4 3 2 4 2 +--R 3u w x + 5w x - u x + 15u w x + (5u + 95)w x +--R + +--R 2 +--R (- 5u - 95)x +--R * +--R 5 +--R y +--R + +--R 2 8 2 6 2 3 4 +--R (- w x + 95u x - 5w x )y +--R + +--R 2 2 8 2 4 3 2 4 2 2 3 2 4 2 2 2 9 +--R ((5u + 95)w x + 5u w x + (19u w - 5u )x )y - 5w x y + 5u w x y +--R * +--R 5 +--R z +--R + +--R 4 4 11 2 4 10 19 2 4 11 17 +--R (- 3u w x - u w x )y - u w x y +--R + +--R 6 4 8 4 2 4 7 2 6 15 +--R (- 3u w x + (- u - 19u )w x - 19u x )y +--R + +--R 2 4 16 4 2 9 2 2 8 14 +--R (15u w x - 3u w x - u w x )y +--R + +--R 2 4 12 2 11 4 10 4 4 8 13 4 15 2 2 9 12 +--R (- 3u w x - 3u x - w x - u w x )y + (19w x - u w x )y +--R + +--R 4 11 4 2 7 6 4 3 11 +--R (- w x + (- 5w - 15u )x - 5x - 19u x )y +--R + +--R 4 4 13 6 2 6 4 2 2 5 10 +--R (15u w x - 3u w x + (- u - 19u )w x )y +--R + +--R 2 2 14 4 4 8 2 4 7 6 9 +--R (15u w x + (- 5w - 3u )x + (- u w - 5)x - 19x )y +--R + +--R 2 4 12 2 2 10 2 8 4 2 6 8 +--R (19u w x - 3u w x - w x - u w x )y +--R + +--R 2 13 2 4 8 4 4 5 4 4 4 2 3 7 +--R (19w x - u w x + 15u w x - 15u x + (95w - 5u - 95)x )y +--R + +--R 2 9 2 2 6 2 5 6 +--R (- w x - 15u w x - 5w x )y +--R + +--R 4 2 11 2 4 2 4 2 3 5 +--R (15u w x + (19u w - 5u )x - 19u x )y +--R + +--R 2 6 2 2 5 4 2 2 10 2 4 3 2 2 6 2 +--R (- 5w x + (- u - 19)w x )y + (19u w x + 95u w )y - u w x y +--R * +--R 4 +--R z +--R + +--R 4 4 13 21 6 4 10 2 4 8 17 4 2 11 16 +--R - 3u w x y + (- 3u w x - 19u w x )y - 3u w x y +--R + +--R 2 4 13 4 12 15 +--R (- 3u w x - w x )y +--R + +--R 4 13 2 4 10 2 9 4 8 4 4 5 13 +--R (- w x - 15u w x - 15u x - 5w x - 19u w x )y +--R + +--R 4 13 6 2 8 2 2 6 12 +--R (95w x - 3u w x - 19u w x )y +--R + +--R 4 4 10 2 4 9 8 11 2 2 11 2 10 10 +--R (- 3u w x + (- u - 24)w x - 19x )y + (- 3u w x - w x )y +--R + +--R 2 4 10 4 6 2 4 5 4 9 +--R (- u w x - 15u x - 5u w x - 95x )y +--R + +--R 2 11 2 4 10 2 2 8 2 6 4 2 3 8 +--R (- w x + 95u w x - 15u w x - 5w x - 19u w x )y +--R + +--R 2 11 2 4 6 2 5 7 4 2 8 2 2 7 6 +--R (95w x - 5u w x - 19u x )y + (- 3u w x + (- u - 24)w x )y +--R + +--R 2 4 2 2 5 2 2 8 2 2 3 4 2 2 8 3 +--R (95u w x - 95u x)y + (- u w x + (- 5u - 95)w x )y + 95u w x y +--R + +--R 2 2 4 2 +--R - 5u w x y +--R * +--R 3 +--R z +--R + +--R 2 4 10 19 2 4 15 17 2 4 11 4 10 4 4 7 15 +--R - 19u w x y - 3u w x y + (- 15u w x - 5w x - 19u w x )y +--R + +--R 2 2 8 14 4 4 12 4 11 4 10 13 2 2 13 12 +--R - 19u w x y + (- 3u w x - 5w x - 19w x )y - 3u w x y +--R + +--R 4 4 8 2 4 7 6 11 +--R (- 15u w x + (- 5u - 95)w x - 95x )y +--R + +--R 2 2 9 2 8 4 2 5 10 2 4 8 2 4 7 9 +--R (- 15u w x - 5w x - 19u w x )y + (- 5u w x - 19u w x )y +--R + +--R 4 2 10 2 9 2 8 8 2 3 7 +--R (- 3u w x - 5w x - 19w x )y - 95u x y +--R + +--R 4 2 6 2 2 5 6 2 2 6 2 2 5 4 +--R (- 15u w x + (- 5u - 95)w x )y + (- 5u w x - 19u w x )y +--R * +--R 2 +--R z +--R + +--R 2 4 13 17 4 12 15 4 4 10 4 8 13 2 2 11 12 +--R - 15u w x y - 19w x y + (- 15u w x - 95w x )y - 15u w x y +--R + +--R 2 4 9 11 2 10 10 2 4 5 9 4 2 8 2 6 8 +--R - 19u w x y - 19w x y - 95u w x y + (- 15u w x - 95w x )y +--R + +--R 2 2 7 6 2 2 3 4 +--R - 19u w x y - 95u w x y +--R * +--R z +--R + +--R 4 10 15 2 4 7 11 2 8 10 2 2 5 6 +--R - 95w x y - 95u w x y - 95w x y - 95u w x y +--R Type: Polynomial(Integer) +--E 13 + +--S 14 of 45 +t5f:=factor t5 +--R +--R +--R (14) +--R - +--R 2 3 4 2 2 2 2 3 4 2 2 4 2 2 +--R (z + x y + u )((y + x)z + 3u x y z + 19y )(u y z + x z + 5) +--R * +--R 4 3 2 2 4 5 6 2 3 5 3 2 3 +--R (w z - x y z - w x y - w x y)(x z - y z - x y ) +--R Type: Factored(Polynomial(Integer)) +--E 14 + +--S 15 of 45 +t5-t5f +--R +--R +--R (15) 0 +--R Type: Factored(Polynomial(Integer)) +--E 15 + +--S 16 of 45 +t6:=(w^4*z^6 + y^2*z^3 - w^2*x^2*y^2*z^2 + x^5*z - x^4*y^2 - w^3*x^3*y) +--R +--R +--R 4 6 2 3 2 2 2 2 5 4 2 3 3 +--R (16) w z + y z - w x y z + x z - x y - w x y +--R Type: Polynomial(Integer) +--E 16 + +--S 17 of 45 +t6f:=factor t6 +--R +--R +--R 4 6 2 3 2 2 2 2 5 4 2 3 3 +--R (17) w z + y z - w x y z + x z - x y - w x y +--R Type: Factored(Polynomial(Integer)) +--E 17 + +--S 18 of 45 +t6-t6f +--R +--R +--R (18) 0 +--R Type: Factored(Polynomial(Integer)) +--E 18 + +--S 19 of 45 +t7:=(z + y + x - 3)^3 *(z + y + x - 2)^2 *_ + (-15*y^2*z^16 + 29*w^4*x^12*y^12*z^3 + 21*x^3*z^2 + 3*w^15*y^20) +--R +--R +--R (19) +--R 2 21 3 2 20 +--R - 15y z + (- 75y + (- 75x + 195)y )z +--R + +--R 4 3 2 2 19 +--R (- 150y + (- 300x + 780)y + (- 150x + 780x - 1005)y )z +--R + +--R 5 4 2 3 +--R - 150y + (- 450x + 1170)y + (- 450x + 2340x - 3015)y +--R + +--R 3 2 2 +--R (- 150x + 1170x - 3015x + 2565)y +--R * +--R 18 +--R z +--R + +--R 6 5 2 4 +--R - 75y + (- 300x + 780)y + (- 450x + 2340x - 3015)y +--R + +--R 3 2 3 +--R (- 300x + 2340x - 6030x + 5130)y +--R + +--R 4 3 2 2 +--R (- 75x + 780x - 3015x + 5130x - 3240)y +--R * +--R 17 +--R z +--R + +--R 7 6 2 5 +--R - 15y + (- 75x + 195)y + (- 150x + 780x - 1005)y +--R + +--R 3 2 4 +--R (- 150x + 1170x - 3015x + 2565)y +--R + +--R 4 3 2 3 +--R (- 75x + 780x - 3015x + 5130x - 3240)y +--R + +--R 5 4 3 2 2 +--R (- 15x + 195x - 1005x + 2565x - 3240x + 1620)y +--R * +--R 16 +--R z +--R + +--R 4 12 12 8 4 12 13 4 13 4 12 12 3 7 +--R 29w x y z + (145w x y + (145w x - 377w x )y + 21x )z +--R + +--R 4 12 14 4 13 4 12 13 +--R 290w x y + (580w x - 1508w x )y +--R + +--R 4 14 4 13 4 12 12 3 4 3 +--R (290w x - 1508w x + 1943w x )y + 105x y + 105x - 273x +--R * +--R 6 +--R z +--R + +--R 15 20 4 12 15 4 13 4 12 14 +--R 3w y + 290w x y + (870w x - 2262w x )y +--R + +--R 4 14 4 13 4 12 13 +--R (870w x - 4524w x + 5829w x )y +--R + +--R 4 15 4 14 4 13 4 12 12 3 2 +--R (290w x - 2262w x + 5829w x - 4959w x )y + 210x y +--R + +--R 4 3 5 4 3 +--R (420x - 1092x )y + 210x - 1092x + 1407x +--R * +--R 5 +--R z +--R + +--R 15 21 15 15 20 4 12 16 +--R 15w y + (15w x - 39w )y + 145w x y +--R + +--R 4 13 4 12 15 4 14 4 13 4 12 14 +--R (580w x - 1508w x )y + (870w x - 4524w x + 5829w x )y +--R + +--R 4 15 4 14 4 13 4 12 13 +--R (580w x - 4524w x + 11658w x - 9918w x )y +--R + +--R 4 16 4 15 4 14 4 13 4 12 12 3 3 +--R (145w x - 1508w x + 5829w x - 9918w x + 6264w x )y + 210x y +--R + +--R 4 3 2 5 4 3 6 5 +--R (630x - 1638x )y + (630x - 3276x + 4221x )y + 210x - 1638x +--R + +--R 4 3 +--R 4221x - 3591x +--R * +--R 4 +--R z +--R + +--R 15 22 15 15 21 15 2 15 15 20 +--R 30w y + (60w x - 156w )y + (30w x - 156w x + 201w )y +--R + +--R 4 12 17 4 13 4 12 16 +--R 29w x y + (145w x - 377w x )y +--R + +--R 4 14 4 13 4 12 15 +--R (290w x - 1508w x + 1943w x )y +--R + +--R 4 15 4 14 4 13 4 12 14 +--R (290w x - 2262w x + 5829w x - 4959w x )y +--R + +--R 4 16 4 15 4 14 4 13 4 12 13 +--R (145w x - 1508w x + 5829w x - 9918w x + 6264w x )y +--R + +--R 4 17 4 16 4 15 4 14 4 13 4 12 12 +--R (29w x - 377w x + 1943w x - 4959w x + 6264w x - 3132w x )y +--R + +--R 3 4 4 3 3 5 4 3 2 +--R 105x y + (420x - 1092x )y + (630x - 3276x + 4221x )y +--R + +--R 6 5 4 3 7 6 5 4 +--R (420x - 3276x + 8442x - 7182x )y + 105x - 1092x + 4221x - 7182x +--R + +--R 3 +--R 4536x +--R * +--R 3 +--R z +--R + +--R 15 23 15 15 22 15 2 15 15 21 +--R 30w y + (90w x - 234w )y + (90w x - 468w x + 603w )y +--R + +--R 15 3 15 2 15 15 20 3 5 4 3 4 +--R (30w x - 234w x + 603w x - 513w )y + 21x y + (105x - 273x )y +--R + +--R 5 4 3 3 6 5 4 3 2 +--R (210x - 1092x + 1407x )y + (210x - 1638x + 4221x - 3591x )y +--R + +--R 7 6 5 4 3 8 7 6 +--R (105x - 1092x + 4221x - 7182x + 4536x )y + 21x - 273x + 1407x +--R + +--R 5 4 3 +--R - 3591x + 4536x - 2268x +--R * +--R 2 +--R z +--R + +--R 15 24 15 15 23 15 2 15 15 22 +--R 15w y + (60w x - 156w )y + (90w x - 468w x + 603w )y +--R + +--R 15 3 15 2 15 15 21 +--R (60w x - 468w x + 1206w x - 1026w )y +--R + +--R 15 4 15 3 15 2 15 15 20 +--R (15w x - 156w x + 603w x - 1026w x + 648w )y +--R * +--R z +--R + +--R 15 25 15 15 24 15 2 15 15 23 +--R 3w y + (15w x - 39w )y + (30w x - 156w x + 201w )y +--R + +--R 15 3 15 2 15 15 22 +--R (30w x - 234w x + 603w x - 513w )y +--R + +--R 15 4 15 3 15 2 15 15 21 +--R (15w x - 156w x + 603w x - 1026w x + 648w )y +--R + +--R 15 5 15 4 15 3 15 2 15 15 20 +--R (3w x - 39w x + 201w x - 513w x + 648w x - 324w )y +--R Type: Polynomial(Integer) +--E 19 + +--S 20 of 45 +t7f:=factor t7 +--R +--R +--R (20) +--R 3 2 2 16 4 12 12 3 3 2 15 20 +--R - (z + y + x - 3) (z + y + x - 2) (15y z - 29w x y z - 21x z - 3w y ) +--R Type: Factored(Polynomial(Integer)) +--E 20 + +--S 21 of 45 +t7-t7f +--R +--R +--R (21) 0 +--R Type: Factored(Polynomial(Integer)) +--E 21 + +--S 22 of 45 +t8:=(-z^31 - w^12*z^20 + y^18 - y^14 + x^2*y^2 + x^21 + w^2)*_ + u^4*x*z^2*(6*w^2*y^3*z^2 + 18*u^2*w^3*x*z^2 + 15*u*z^2 + 10*u^2*w*x*y^3) +--R +--R +--R (22) +--R 4 2 3 6 3 2 5 35 6 2 3 33 +--R (- 6u w x y - 18u w x - 15u x)z - 10u w x y z +--R + +--R 4 14 3 6 15 2 5 12 24 6 13 2 3 22 +--R (- 6u w x y - 18u w x - 15u w x)z - 10u w x y z +--R + +--R 4 2 21 6 3 2 5 18 4 2 17 +--R 6u w x y + (18u w x + 15u x)y - 6u w x y +--R + +--R 6 3 2 5 14 4 2 3 5 4 2 22 4 4 3 +--R (- 18u w x - 15u x)y + 6u w x y + (6u w x + 6u w x)y +--R + +--R 6 3 4 5 3 2 6 3 23 5 22 6 5 2 5 2 +--R (18u w x + 15u x )y + 18u w x + 15u x + 18u w x + 15u w x +--R * +--R 4 +--R z +--R + +--R 6 2 21 6 2 17 6 4 5 6 23 6 3 2 3 2 +--R (10u w x y - 10u w x y + 10u w x y + (10u w x + 10u w x )y )z +--R Type: Polynomial(Integer) +--E 22 + +--S 23 of 45 +t8f:=factor t8 +--R +--R +--R (23) +--R - +--R 4 2 2 3 2 3 2 2 3 +--R u x z ((6w y + 18u w x + 15u)z + 10u w x y ) +--R * +--R 31 12 20 18 14 2 2 21 2 +--R (z + w z - y + y - x y - x - w ) +--R Type: Factored(Polynomial(Integer)) +--E 23 + +--S 24 of 45 +t8-t8f +--R +--R +--R (24) 0 +--R Type: Factored(Polynomial(Integer)) +--E 24 + +--S 25 of 45 +t9:=(-44*u*w*x*y^4*z^4 - 25*u^2*w^3*y*z^4 + 8*u*w*x^3*z^4 - 32*u^2*w^4*y*4*z^3_ + + 48*u^2*x^2*y^3*z^3 - 12*y^3*z^2 + 2*u^2*w*x^2*y^2 - 11*u*w^2*x^3*y_ + - 4*w^2*x) +--R +--R +--R (25) +--R 4 2 3 3 4 2 2 3 2 4 3 3 2 +--R (- 44u w x y - 25u w y + 8u w x )z + (48u x y - 128u w y)z - 12y z +--R + +--R 2 2 2 2 3 2 +--R 2u w x y - 11u w x y - 4w x +--R Type: Polynomial(Integer) +--E 25 + +--S 26 of 45 +t9f:=factor t9 +--R +--R +--R (26) +--R - +--R 4 2 3 3 4 2 2 3 2 4 3 3 2 +--R (44u w x y + 25u w y - 8u w x )z + (- 48u x y + 128u w y)z + 12y z +--R + +--R 2 2 2 2 3 2 +--R - 2u w x y + 11u w x y + 4w x +--R Type: Factored(Polynomial(Integer)) +--E 26 + +--S 27 of 45 +t9-t9f +--R +--R +--R (27) 0 +--R Type: Factored(Polynomial(Integer)) +--E 27 + +--S 28 of 45 +t10:=(31*u^2*x*z + 35*w^2*y^2 + 6*x*y + 40*w*x^2)*_ + (u^2*w^2*x*y^2*z^2 + 24*u^2*w*x*y^2*z^2 + 12*u^2*x*y^2*z^2 +_ + 24*u^2*x^2*y*z^2 + 43*w*x*y*z^2 + 31*w^2*y*z^2 + 8*u^2*w^2*z^2 +_ + 44*u*w^2*z^2 + 37*u^2*y^2*z + 41*y^2*z + 12*w*x^2*y*z + 21*u^2*w*x*y*z +_ + 23*x*y*z + 47*u^2*w^2*z + 13*u*w^2*x^2*y^2 + 22*x*y^2 + 42*u^2*w^2*y^2 +_ + 29*w^2*y^2 + 27*u*w^2*x^2*y + 37*w^2*x*z + 39*u*w*x*z + 43*u*x^2*y +_ + 24*x*y + 9*u^2*w*x^2 + 22*u^2*w^2) +--R +--R +--R (28) +--R 4 2 4 4 2 2 4 3 2 2 2 2 +--R (31u w + 744u w + 372u )x y + (744u x + 1333u w x + 961u w x)y +--R + +--R 4 3 2 +--R (248u + 1364u )w x +--R * +--R 3 +--R z +--R + +--R 2 4 2 3 2 2 4 +--R (35u w + 840u w + 420u w )x y +--R + +--R 2 2 2 2 2 3 4 3 +--R ((846u w + 144u w + 72u )x + 1505w x + 1085w )y +--R + +--R 2 3 2 2 2 2 3 2 +--R (40u w + 960u w + 480u w + 144u )x + 258w x +--R + +--R 2 4 2 2 4 +--R (186w + 1147u + 1271u )x + (280u + 1540u)w +--R * +--R 2 +--R y +--R + +--R 2 4 2 2 3 3 4 2 2 +--R 960u w x + (1720w + 372u w)x + (1240w + 651u w + 713u )x +--R + +--R 2 2 +--R (48u + 264u)w x +--R * +--R y +--R + +--R 2 3 2 2 3 2 4 2 +--R ((320u + 1760u)w + 1147u w + 1209u w)x + 1457u w x +--R * +--R 2 +--R z +--R + +--R 2 2 4 3 2 2 3 2 2 3 +--R (1295u + 1435)w y + (420w x + (735u w + 805w + 222u + 246)x)y +--R + +--R 3 2 3 2 2 2 +--R (403u w + 72w)x + ((1606u + 1640)w + 682u + 138)x +--R + +--R 4 3 4 2 2 2 4 +--R (1295w + 1365u w + (1302u + 899u )w )x + 1645u w +--R * +--R 2 +--R y +--R + +--R 2 4 3 2 2 3 3 +--R 480w x + ((837u + 840u )w + 920w + 1333u )x +--R + +--R 2 2 2 2 2 +--R (222w + 234u w + 744u )x + 282u w x +--R * +--R y +--R + +--R 3 2 4 3 2 3 2 4 2 +--R (1480w + 1560u w + 279u w)x + 1880u w x + 682u w x +--R * +--R z +--R + +--R 4 2 2 2 4 4 +--R (455u w x + 770w x + (1470u + 1015)w )y +--R + +--R 2 3 4 2 2 2 2 3 +--R (78u w x + (945u w + 1505u w + 132)x + (252u + 1014)w x)y +--R + +--R 3 4 2 3 2 3 2 +--R 520u w x + (162u w + 880w + 258u)x + ((1995u + 1160)w + 144)x +--R + +--R 2 4 +--R 770u w +--R * +--R 2 +--R y +--R + +--R 3 4 2 3 2 2 2 2 4 +--R ((1080u w + 1720u w)x + (54u + 960)w x + 132u w x)y + 360u w x +--R + +--R 2 3 2 +--R 880u w x +--R Type: Polynomial(Integer) +--E 28 + +--S 29 of 45 +t10f:=factor t10 +--R +--R +--R (29) +--R 2 2 2 2 +--R (31u x z + 35w y + 6x y + 40w x ) +--R * +--R 2 2 2 2 2 2 2 2 2 2 2 +--R ((u w + 24u w + 12u )x y + (24u x + 43w x + 31w )y + (8u + 44u)w )z +--R + +--R 2 2 2 2 2 2 2 +--R ((37u + 41)y + (12w x + (21u w + 23)x)y + (37w + 39u w)x + 47u w )z +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (13u w x + 22x + (42u + 29)w )y + ((27u w + 43u)x + 24x)y + 9u w x +--R + +--R 2 2 +--R 22u w +--R Type: Factored(Polynomial(Integer)) +--E 29 + +--S 30 of 45 +t10-t10f +--R +--R +--R (30) 0 +--R Type: Factored(Polynomial(Integer)) +--E 30 + +--S 31 of 45 +t11:=x*y*(-13*u^3*w^2*x*y*z^3 + w^3*z^3 + 4*u*x*y^2 + 47*x*y)*_ + (43*u*x^3*y^3*z^3 + 36*u^2*w^3*x*y*z^3 + 14*w^3*x^3*y^3*z^2 -_ + 29*w^3*x*y^3*z^2 - 20*u^2*w^2*x^2*y^2*z^2 + 36*u^2*w*x*y^3*z -_ + 48*u*w*x^3*y^2*z + 5*u*w*x^2*y^3 + 36*u*w^2*y^3 - 9*u*w*y^3 -_ + 23*u*w*x^3*y^2 + 46*u*x^3*y^2 + 8*x*y^2 + 31*u^2*w^3*y^2 -_ + 9*u^2*y^2 + 45*x^3 - 46*u^2*w*x) +--R +--R +--R (31) +--R 4 2 5 5 3 4 4 5 5 3 3 2 6 2 2 6 +--R (- 559u w x y + 43u w x y - 468u w x y + 36u w x y )z +--R + +--R 3 5 5 3 5 3 5 6 5 4 4 6 2 4 +--R (- 182u w x + 377u w x )y + ((14w + 260u w )x - 29w x )y +--R + +--R 2 5 3 3 +--R - 20u w x y +--R * +--R 5 +--R z +--R + +--R 5 3 3 5 4 3 5 2 4 2 4 4 4 3 4 +--R (- 468u w x y + (624u w x + 36u w x )y - 48u w x y )z +--R + +--R 2 5 6 5 4 3 4 4 4 4 3 2 5 +--R 172u x y + (2021u x - 65u w x + (- 468u w + 117u w )x )y +--R + +--R 4 3 4 2 5 4 3 3 3 2 3 +--R (299u w - 598u w )x + (5u w + 144u w - 104u w )x +--R + +--R 5 5 5 2 2 5 4 +--R (- 403u w + 117u w )x + (36u w - 9u w )x +--R * +--R 4 +--R y +--R + +--R 4 3 4 2 3 3 3 2 2 6 2 3 3 +--R ((- 23u w + 46u w )x + 1692u w x + 8w x + (31u w - 9u w )x)y +--R + +--R 3 2 5 5 3 3 2 3 4 2 4 2 +--R (- 585u w x + 598u w x )y + (45w x - 46u w x )y +--R * +--R 3 +--R z +--R + +--R 3 5 3 3 6 3 5 3 2 4 3 3 5 +--R (56u w x - 116u w x )y + (658w x - 80u w x - 1363w x )y +--R + +--R 2 2 4 4 +--R - 940u w x y +--R * +--R 2 +--R z +--R + +--R 3 3 6 2 5 2 3 5 5 4 +--R (144u w x y + (- 192u w x + 1692u w x )y - 2256u w x y )z +--R + +--R 2 4 2 2 2 2 6 +--R (20u w x + (144u w - 36u w)x )y +--R + +--R 2 2 5 4 3 +--R (- 92u w + 184u )x + 235u w x + 32u x +--R + +--R 3 3 2 3 2 +--R (124u w + 1692u w - 423u w - 36u )x +--R * +--R 5 +--R y +--R + +--R 5 3 2 3 2 2 4 +--R ((- 1081u w + 2162u)x + 376x + (1457u w - 423u )x )y +--R + +--R 5 3 3 3 5 2 3 2 +--R (180u x - 184u w x )y + (2115x - 2162u w x )y +--R Type: Polynomial(Integer) +--E 31 + +--S 32 of 45 +t11f:=factor t11 +--R +--R +--R (32) +--R - +--R 3 2 3 3 2 +--R x y((13u w x y - w )z - 4u x y - 47x y) +--R * +--R 3 3 2 3 3 3 3 3 3 2 2 2 2 2 +--R (43u x y + 36u w x y)z + ((14w x - 29w x)y - 20u w x y )z +--R + +--R 2 3 3 2 2 2 3 +--R (36u w x y - 48u w x y )z + (5u w x + 36u w - 9u w)y +--R + +--R 3 2 3 2 2 3 2 +--R ((- 23u w + 46u)x + 8x + 31u w - 9u )y + 45x - 46u w x +--R Type: Factored(Polynomial(Integer)) +--E 32 + +--S 33 of 45 +t11-t11f +--R +--R +--R (33) 0 +--R Type: Factored(Polynomial(Integer)) +--E 33 + +--S 34 of 45 +t12:=(z + y + x - 3)^3 +--R +--R +--R (34) +--R 3 2 2 2 3 +--R z + (3y + 3x - 9)z + (3y + (6x - 18)y + 3x - 18x + 27)z + y +--R + +--R 2 2 3 2 +--R (3x - 9)y + (3x - 18x + 27)y + x - 9x + 27x - 27 +--R Type: Polynomial(Integer) +--E 34 + +--S 35 of 45 +t12f:=factor t12 +--R +--R +--R 3 +--R (35) (z + y + x - 3) +--R Type: Factored(Polynomial(Integer)) +--E 35 + +--S 36 of 45 +t12-t12f +--R +--R +--R (36) 0 +--R Type: Factored(Polynomial(Integer)) +--E 36 + +--S 37 of 45 +t13:=(3*z^3 + 2*w*z - 9*y^3 - y^2 + 45*x^3)*(w^2*z^3 + 47*x*y - w^2) +--R +--R +--R (37) +--R 2 6 3 4 2 3 2 2 2 3 2 3 +--R 3w z + 2w z + (- 9w y - w y + 141x y + 45w x - 3w )z +--R + +--R 3 4 2 3 2 2 4 2 3 +--R (94w x y - 2w )z - 423x y + (- 47x + 9w )y + w y + 2115x y - 45w x +--R Type: Polynomial(Integer) +--E 37 + +--S 38 of 45 +t13f:=factor t13 +--R +--R +--R 3 3 2 3 2 3 2 +--R (38) (3z + 2w z - 9y - y + 45x )(w z + 47x y - w ) +--R Type: Factored(Polynomial(Integer)) +--E 38 + +--S 39 of 45 +t13-t13f +--R +--R +--R (39) 0 +--R Type: Factored(Polynomial(Integer)) +--E 39 + +--S 40 of 45 +t14:=(-18*x^4*y^5 + 22*y^5 - 26*x^3*y^4 - 38*x^2*y^4 + 29*x^2*y^3 -_ + 41*x^4*y^2 + 37*x^4)*(33*x^5*y^6 + 11*y^2 + 35*x^3*y - 22*x^4) +--R +--R +--R (40) +--R 9 5 11 8 7 10 7 9 9 8 +--R (- 594x + 726x )y + (- 858x - 1254x )y + 957x y - 1353x y +--R + +--R 4 7 9 7 3 2 6 +--R (- 198x + 242)y + (1221x - 630x + 484x - 418x )y +--R + +--R 8 6 5 4 2 5 +--R (396x - 910x - 1330x - 484x + 319x )y +--R + +--R 7 6 5 4 4 7 6 3 +--R (572x + 836x + 1015x - 451x )y + (- 1435x - 638x )y +--R + +--R 8 4 2 7 8 +--R (902x + 407x )y + 1295x y - 814x +--R Type: Polynomial(Integer) +--E 40 + +--S 41 of 45 +t14f:=factor t14 +--R +--R +--R (41) +--R - +--R 4 5 3 2 4 2 3 4 2 4 +--R ((18x - 22)y + (26x + 38x )y - 29x y + 41x y - 37x ) +--R * +--R 5 6 2 3 4 +--R (33x y + 11y + 35x y - 22x ) +--R Type: Factored(Polynomial(Integer)) +--E 41 + +--S 42 of 45 +t14-t14f +--R +--R +--R (42) 0 +--R Type: Factored(Polynomial(Integer)) +--E 42 + +--S 43 of 45 +t15:=x^6*y^3*z^2*(3*z^3 + 2*w*z - 8*x*y^2 + 14*w^2*y^2 - y^2 + 18*x^3*y)*_ + (-12*w^2*x*y*z^3 + w^2*z^3 + 3*x*y^2 + 29*x - w^2) +--R +--R +--R (43) +--R 2 7 4 2 6 3 8 3 7 4 3 6 3 6 +--R (- 36w x y + 3w x y )z + (- 24w x y + 2w x y )z +--R + +--R 2 8 4 2 7 6 +--R (96w x + (- 168w + 12w )x )y +--R + +--R 2 10 2 7 4 2 6 5 2 9 4 +--R (- 216w x + (- 8w + 9)x + (14w - w )x )y + 18w x y +--R + +--R 7 2 6 3 +--R (87x - 3w x )y +--R * +--R 5 +--R z +--R + +--R 7 5 7 3 6 3 3 +--R (6w x y + (58w x - 2w x )y )z +--R + +--R 8 2 7 7 10 6 +--R (- 24x + (42w - 3)x )y + 54x y +--R + +--R 8 2 7 4 2 6 5 10 2 9 4 +--R (- 232x + (414w - 29)x + (- 14w + w )x )y + (522x - 18w x )y +--R * +--R 2 +--R z +--R Type: Polynomial(Integer) +--E 43 + +--S 44 of 45 +t15f:=factor t15 +--R +--R +--R (44) +--R - +--R 6 3 2 3 2 2 3 +--R x y z (3z + 2w z + (- 8x + 14w - 1)y + 18x y) +--R * +--R 2 2 3 2 2 +--R ((12w x y - w )z - 3x y - 29x + w ) +--R Type: Factored(Polynomial(Integer)) +--E 44 + +--S 45 of 45 +t15-t15f +--R +--R +--R (45) 0 +--R Type: Factored(Polynomial(Integer)) +--E 45 +)spool +)lisp (bye) + +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem[Wang 78]{Wang78} Wang, Paul S.\\ +``An Improved Multivariate Polynomial Factoring Algorithm''\\ +Mathematics of Computation, Vol 32, No 144 Oct 1978, pp1215-1231 +\verb|www.ams.org/journals/mcom/1978-32-144/S0025-5718-1978-0568284-3/| +\verb|S0025-5718-1978-0568284-3.pdf| +\end{thebibliography} +\end{document}