1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
|
\begin{patch}{DistributedMultivariatePolynomialXmpPagePatch1}
\begin{paste}{DistributedMultivariatePolynomialXmpPageFull1}{DistributedMultivariatePolynomialXmpPageEmpty1}
\pastebutton{DistributedMultivariatePolynomialXmpPageFull1}{\hidepaste}
\tab{5}\spadcommand{(d1,d2,d3) : DMP([z,y,x],FRAC INT)\bound{d1dec d2dec d3dec }}
\indentrel{3}\begin{verbatim}
Type: Void
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{DistributedMultivariatePolynomialXmpPageEmpty1}
\begin{paste}{DistributedMultivariatePolynomialXmpPageEmpty1}{DistributedMultivariatePolynomialXmpPagePatch1}
\pastebutton{DistributedMultivariatePolynomialXmpPageEmpty1}{\showpaste}
\tab{5}\spadcommand{(d1,d2,d3) : DMP([z,y,x],FRAC INT)\bound{d1dec d2dec d3dec }}
\end{paste}\end{patch}
\begin{patch}{DistributedMultivariatePolynomialXmpPagePatch2}
\begin{paste}{DistributedMultivariatePolynomialXmpPageFull2}{DistributedMultivariatePolynomialXmpPageEmpty2}
\pastebutton{DistributedMultivariatePolynomialXmpPageFull2}{\hidepaste}
\tab{5}\spadcommand{d1 := -4*z + 4*y**2*x + 16*x**2 + 1\bound{d1 }\free{d1dec }}
\indentrel{3}\begin{verbatim}
2 2
(2) - 4z + 4y x + 16x + 1
Type: DistributedMultivariatePolynomial([z,y,x],Fraction Integer)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{DistributedMultivariatePolynomialXmpPageEmpty2}
\begin{paste}{DistributedMultivariatePolynomialXmpPageEmpty2}{DistributedMultivariatePolynomialXmpPagePatch2}
\pastebutton{DistributedMultivariatePolynomialXmpPageEmpty2}{\showpaste}
\tab{5}\spadcommand{d1 := -4*z + 4*y**2*x + 16*x**2 + 1\bound{d1 }\free{d1dec }}
\end{paste}\end{patch}
\begin{patch}{DistributedMultivariatePolynomialXmpPagePatch3}
\begin{paste}{DistributedMultivariatePolynomialXmpPageFull3}{DistributedMultivariatePolynomialXmpPageEmpty3}
\pastebutton{DistributedMultivariatePolynomialXmpPageFull3}{\hidepaste}
\tab{5}\spadcommand{d2 := 2*z*y**2 + 4*x + 1\bound{d2 }\free{d2dec }}
\indentrel{3}\begin{verbatim}
2
(3) 2z y + 4x + 1
Type: DistributedMultivariatePolynomial([z,y,x],Fraction Integer)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{DistributedMultivariatePolynomialXmpPageEmpty3}
\begin{paste}{DistributedMultivariatePolynomialXmpPageEmpty3}{DistributedMultivariatePolynomialXmpPagePatch3}
\pastebutton{DistributedMultivariatePolynomialXmpPageEmpty3}{\showpaste}
\tab{5}\spadcommand{d2 := 2*z*y**2 + 4*x + 1\bound{d2 }\free{d2dec }}
\end{paste}\end{patch}
\begin{patch}{DistributedMultivariatePolynomialXmpPagePatch4}
\begin{paste}{DistributedMultivariatePolynomialXmpPageFull4}{DistributedMultivariatePolynomialXmpPageEmpty4}
\pastebutton{DistributedMultivariatePolynomialXmpPageFull4}{\hidepaste}
\tab{5}\spadcommand{d3 := 2*z*x**2 - 2*y**2 - x\bound{d3 }\free{d3dec }}
\indentrel{3}\begin{verbatim}
2 2
(4) 2z x - 2y - x
Type: DistributedMultivariatePolynomial([z,y,x],Fraction Integer)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{DistributedMultivariatePolynomialXmpPageEmpty4}
\begin{paste}{DistributedMultivariatePolynomialXmpPageEmpty4}{DistributedMultivariatePolynomialXmpPagePatch4}
\pastebutton{DistributedMultivariatePolynomialXmpPageEmpty4}{\showpaste}
\tab{5}\spadcommand{d3 := 2*z*x**2 - 2*y**2 - x\bound{d3 }\free{d3dec }}
\end{paste}\end{patch}
\begin{patch}{DistributedMultivariatePolynomialXmpPagePatch5}
\begin{paste}{DistributedMultivariatePolynomialXmpPageFull5}{DistributedMultivariatePolynomialXmpPageEmpty5}
\pastebutton{DistributedMultivariatePolynomialXmpPageFull5}{\hidepaste}
\tab{5}\spadcommand{groebner [d1,d2,d3]\free{d1 d2 d3 }}
\indentrel{3}\begin{verbatim}
(5)
[
1568 6 1264 5 6 4 182 3 2047 2
z - ���� x - ���� x + ��� x + ��� x - ���� x
2745 305 305 549 610
+
103 2857
- ���� x - �����
2745 10980
,
2 112 6 84 5 1264 4 13 3 84 2
y + ���� x - ��� x - ���� x - ��� x + ��� x
2745 305 305 549 305
+
1772 2
���� x + ����
2745 2745
,
7 29 6 17 4 11 3 1 2 15 1
x + �� x - �� x - �� x + �� x + �� x + �]
4 16 8 32 16 4
Type: List DistributedMultivariatePolynomial([z,y,x],Fraction Integer)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{DistributedMultivariatePolynomialXmpPageEmpty5}
\begin{paste}{DistributedMultivariatePolynomialXmpPageEmpty5}{DistributedMultivariatePolynomialXmpPagePatch5}
\pastebutton{DistributedMultivariatePolynomialXmpPageEmpty5}{\showpaste}
\tab{5}\spadcommand{groebner [d1,d2,d3]\free{d1 d2 d3 }}
\end{paste}\end{patch}
\begin{patch}{DistributedMultivariatePolynomialXmpPagePatch6}
\begin{paste}{DistributedMultivariatePolynomialXmpPageFull6}{DistributedMultivariatePolynomialXmpPageEmpty6}
\pastebutton{DistributedMultivariatePolynomialXmpPageFull6}{\hidepaste}
\tab{5}\spadcommand{(n1,n2,n3) : HDMP([z,y,x],FRAC INT)\bound{ndec }}
\indentrel{3}\begin{verbatim}
Type: Void
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{DistributedMultivariatePolynomialXmpPageEmpty6}
\begin{paste}{DistributedMultivariatePolynomialXmpPageEmpty6}{DistributedMultivariatePolynomialXmpPagePatch6}
\pastebutton{DistributedMultivariatePolynomialXmpPageEmpty6}{\showpaste}
\tab{5}\spadcommand{(n1,n2,n3) : HDMP([z,y,x],FRAC INT)\bound{ndec }}
\end{paste}\end{patch}
\begin{patch}{DistributedMultivariatePolynomialXmpPagePatch7}
\begin{paste}{DistributedMultivariatePolynomialXmpPageFull7}{DistributedMultivariatePolynomialXmpPageEmpty7}
\pastebutton{DistributedMultivariatePolynomialXmpPageFull7}{\hidepaste}
\tab{5}\spadcommand{(n1,n2,n3) := (d1,d2,d3)\free{ndec }\bound{n }\free{d1 d2 d3 }}
\indentrel{3}\begin{verbatim}
2 2
(7) 2z x - 2y - x
Type: HomogeneousDistributedMultivariatePolynomial([z,y,x],Fraction Integer)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{DistributedMultivariatePolynomialXmpPageEmpty7}
\begin{paste}{DistributedMultivariatePolynomialXmpPageEmpty7}{DistributedMultivariatePolynomialXmpPagePatch7}
\pastebutton{DistributedMultivariatePolynomialXmpPageEmpty7}{\showpaste}
\tab{5}\spadcommand{(n1,n2,n3) := (d1,d2,d3)\free{ndec }\bound{n }\free{d1 d2 d3 }}
\end{paste}\end{patch}
\begin{patch}{DistributedMultivariatePolynomialXmpPagePatch8}
\begin{paste}{DistributedMultivariatePolynomialXmpPageFull8}{DistributedMultivariatePolynomialXmpPageEmpty8}
\pastebutton{DistributedMultivariatePolynomialXmpPageFull8}{\hidepaste}
\tab{5}\spadcommand{groebner [n1,n2,n3]\free{n }}
\indentrel{3}\begin{verbatim}
(8)
4 3 3 2 1 1
[y + 2x - � x + � z - �,
2 2 8
4 29 3 1 2 7 9 1 2 1
x + �� x - � y - � z x - �� x - �, z y + 2x + �,
4 8 4 16 4 2
2 2 1 2 2 1
y x + 4x - z + �, z x - y - � x,
4 2
2 2 2 1 3
z - 4y + 2x - � z - � x]
4 2
Type: List HomogeneousDistributedMultivariatePolynomial([z,y,x],Fraction Integer)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{DistributedMultivariatePolynomialXmpPageEmpty8}
\begin{paste}{DistributedMultivariatePolynomialXmpPageEmpty8}{DistributedMultivariatePolynomialXmpPagePatch8}
\pastebutton{DistributedMultivariatePolynomialXmpPageEmpty8}{\showpaste}
\tab{5}\spadcommand{groebner [n1,n2,n3]\free{n }}
\end{paste}\end{patch}
|
