\begin{patch}{GroebnerFactorizationPackageXmpPagePatch1} \begin{paste}{GroebnerFactorizationPackageXmpPageFull1}{GroebnerFactorizationPackageXmpPageEmpty1} \pastebutton{GroebnerFactorizationPackageXmpPageFull1}{\hidepaste} \tab{5}\spadcommand{mfzn : SQMATRIX(6,DMP([x,y,z],Fraction INT)) := [[0,1,1,1,1,1], [1,0,1,8/3,x,8/3], [1,1,0,1,8/3,y], [1,8/3,1,0,1,8/3], [1,x,8/3,1,0,1], [1,8/3,y,8/3,1,0]]\bound{mfzn }} \indentrel{3}\begin{verbatim} �0 1 1 1 1 1� � � � 8 8� �1 0 1 � x ij � 3 3� � � � 8 � �1 1 0 1 � y� � 3 � � � (1) � 8 8� �1 � 1 0 1 ij � 3 3� � � � 8 � �1 x � 1 0 1� � 3 � � � � 8 8 � �1 � y � 1 0� � 3 3 � Type: SquareMatrix(6,DistributedMultivariatePolynomial([x,y,z],Fraction Integer)) \end{verbatim} \indentrel{-3}\end{paste}\end{patch} \begin{patch}{GroebnerFactorizationPackageXmpPageEmpty1} \begin{paste}{GroebnerFactorizationPackageXmpPageEmpty1}{GroebnerFactorizationPackageXmpPagePatch1} \pastebutton{GroebnerFactorizationPackageXmpPageEmpty1}{\showpaste} \tab{5}\spadcommand{mfzn : SQMATRIX(6,DMP([x,y,z],Fraction INT)) := [[0,1,1,1,1,1], [1,0,1,8/3,x,8/3], [1,1,0,1,8/3,y], [1,8/3,1,0,1,8/3], [1,x,8/3,1,0,1], [1,8/3,y,8/3,1,0]]\bound{mfzn }} \end{paste}\end{patch} \begin{patch}{GroebnerFactorizationPackageXmpPagePatch2} \begin{paste}{GroebnerFactorizationPackageXmpPageFull2}{GroebnerFactorizationPackageXmpPageEmpty2} \pastebutton{GroebnerFactorizationPackageXmpPageFull2}{\hidepaste} \tab{5}\spadcommand{eq := determinant mfzn\free{mfzn }\bound{eq }} \indentrel{3}\begin{verbatim} (2) 2 2 22 2 25 2 22 2 388 250 - x y + �� x y - �� x + �� x y - ��� x y - ��� x 3 9 3 9 27 + 25 2 250 14575 - �� y - ��� y + ����� 9 27 81 Type: DistributedMultivariatePolynomial([x,y,z],Fraction Integer) \end{verbatim} \indentrel{-3}\end{paste}\end{patch} \begin{patch}{GroebnerFactorizationPackageXmpPageEmpty2} \begin{paste}{GroebnerFactorizationPackageXmpPageEmpty2}{GroebnerFactorizationPackageXmpPagePatch2} \pastebutton{GroebnerFactorizationPackageXmpPageEmpty2}{\showpaste} \tab{5}\spadcommand{eq := determinant mfzn\free{mfzn }\bound{eq }} \end{paste}\end{patch} \begin{patch}{GroebnerFactorizationPackageXmpPagePatch3} \begin{paste}{GroebnerFactorizationPackageXmpPageFull3}{GroebnerFactorizationPackageXmpPageEmpty3} \pastebutton{GroebnerFactorizationPackageXmpPageFull3}{\hidepaste} \tab{5}\spadcommand{groebnerFactorize [eq, eval(eq, [x,y,z], [y,z,x]), eval(eq, [x,y,z], [z,x,y])]\free{eq }} \indentrel{3}\begin{verbatim} (3) [ 22 22 22 121 [x y + x z - �� x + y z - �� y - �� z + ���, 3 3 3 3 2 22 25 2 22 25 x z - �� x z + �� x + y z - �� y z + �� y 3 9 3 9 + 22 2 388 250 - �� z + ��� z + ��� 3 9 27 , 2 2 22 2 25 2 22 2 388 250 y z - �� y z + �� y - �� y z + ��� y z + ��� y 3 9 3 9 27 + 25 2 250 14575 �� z + ��� z - ����� 9 27 81 ] , 21994 2 21994 4427 463 [x + y - �����,y - ����� y + ����,z - ���], 5625 5625 675 87 2 1 11 5 265 2 38 265 [x - � x z - �� x - � z + ���,y - z,z - �� z + ���], 2 2 6 18 3 9 25 11 11 11 11 11 [x - ��,y - ��,z - ��], [x - ��,y - ��,z - ��], 9 3 3 3 3 3 5 5 5 19 5 5 [x + �,y + �,z + �], [x - ��,y + �,z + �]] 3 3 3 3 3 3 Type: List List DistributedMultivariatePolynomial([x,y,z],Fraction Integer) \end{verbatim} \indentrel{-3}\end{paste}\end{patch} \begin{patch}{GroebnerFactorizationPackageXmpPageEmpty3} \begin{paste}{GroebnerFactorizationPackageXmpPageEmpty3}{GroebnerFactorizationPackageXmpPagePatch3} \pastebutton{GroebnerFactorizationPackageXmpPageEmpty3}{\showpaste} \tab{5}\spadcommand{groebnerFactorize [eq, eval(eq, [x,y,z], [y,z,x]), eval(eq, [x,y,z], [z,x,y])]\free{eq }} \end{paste}\end{patch}