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\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}
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