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Algebra to solve logic puzzles Convert boolean polynomials to probability
Project: LogicPuzzle2.0
Path: 2021-01-17-124214.sagews
Views: 198License: GPL3
Image: ubuntu2004
Defining X0, X1, X2, X3, X4, X5, X6, X7, X8, X9, X10, X11, X12, X13, X14, X15, X16, X17, X18, X19, X20, X21, X22, X23, X24, X25, X26, X27, X28, X29, X30, X31, X32, X33, X34, X35
36 Free Boolean Algebra generators: X0 = R[0,0], X1 = R[0,1], X2 = R[0,2],..., X35 = R[5,5]
Defining x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22, x23, x24, x25, x26, x27, x28, x29, x30, x31, x32, x33, x34, x35
t
1/3*t^3 - 1/2*t^2 + 7/6*t
Polynomial Sequence with 61 Polynomials in 36 Variables
0
1
2
X1*X8 + X1*X2
Defining x2
x2
Defining x2
Defining x8
0
1
3
X1*X9 + X1*X3
Defining x3
x3
Defining x3
Defining x9
0
1
4
X1*X10 + X1*X4
Defining x4
x4
Defining x4
Defining x10
0
1
5
X1*X11 + X1*X5
Defining x5
x5
Defining x5
Defining x11
0
2
3
X2*X15 + X2*X3
Defining x3
x3
Defining x3
Defining x15
0
2
4
X2*X16 + X2*X4
Defining x4
x4
Defining x4
Defining x16
0
2
5
X2*X17 + X2*X5
Defining x5
x5
Defining x5
Defining x17
0
3
4
X3*X22 + X3*X4
Defining x4
x4
Defining x4
Defining x22
0
3
5
X3*X23 + X3*X5
Defining x5
x5
Defining x5
Defining x23
0
4
5
X4*X29 + X4*X5
Defining x5
x5
Defining x5
Defining x29
1
2
3
X8*X15 + X8*X9
Defining x9
x9
Defining x9
Defining x15
1
2
4
X8*X16 + X8*X10
Defining x10
x10
Defining x10
Defining x16
1
2
5
X8*X17 + X8*X11
Defining x11
x11
Defining x11
Defining x17
1
3
4
X9*X22 + X9*X10
Defining x10
x10
Defining x10
Defining x22
1
3
5
X9*X23 + X9*X11
Defining x11
x11
Defining x11
Defining x23
1
4
5
X10*X29 + X10*X11
Defining x11
x11
Defining x11
Defining x29
2
3
4
X15*X22 + X15*X16
Defining x16
x16
Defining x16
Defining x22
2
3
5
X15*X23 + X15*X17
Defining x17
x17
Defining x17
Defining x23
2
4
5
X16*X29 + X16*X17
Defining x17
x17
Defining x17
Defining x29
3
4
5
X22*X29 + X22*X23
Defining x23
x23
Defining x23
Defining x29
Defining x1, x2, x8
-2*x1*x2*x8 + x1*x8 + x2*x8
Defining X0, X1, X2, X3, X4, X5, X6, X7, X8, X9, X10, X11, X12, X13, X14, X15, X16, X17, X18, X19, X20, X21, X22, X23, X24, X25, X26, X27, X28, X29, X30, X31, X32, X33, X34, X35
36 Free Boolean Algebra generators: X0 = R[0,0], X1 = R[0,1], X2 = R[0,2],..., X35 = R[5,5]
Defining x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22, x23, x24, x25, x26, x27, x28, x29, x30, x31, x32, x33, x34, x35
t
1/3*t^3 - 1/2*t^2 + 7/6*t
Polynomial Sequence with 61 Polynomials in 36 Variables
0
1
2
X1*X8 + X1*X2
Defining x2
x2
Defining x2
Defining x8
Defining x1, x2, x8
-2*x1*x2*x8 + x1*x2 + x1*x8
0
1
3
X1*X9 + X1*X3
Defining x3
x3
Defining x3
Defining x9
Defining x1, x2, x8
-2*x1*x2*x8 + x1*x2 + x1*x8
0
1
4
X1*X10 + X1*X4
Defining x4
x4
Defining x4
Defining x10
Defining x1, x2, x8
-2*x1*x2*x8 + x1*x2 + x1*x8
0
1
5
X1*X11 + X1*X5
Defining x5
x5
Defining x5
Defining x11
Defining x1, x2, x8
-2*x1*x2*x8 + x1*x2 + x1*x8
0
2
3
X2*X15 + X2*X3
Defining x3
x3
Defining x3
Defining x15
Defining x1, x2, x8
-2*x1*x2*x8 + x1*x2 + x1*x8
0
2
4
X2*X16 + X2*X4
Defining x4
x4
Defining x4
Defining x16
Defining x1, x2, x8
-2*x1*x2*x8 + x1*x2 + x1*x8
0
2
5
X2*X17 + X2*X5
Defining x5
x5
Defining x5
Defining x17
Defining x1, x2, x8
-2*x1*x2*x8 + x1*x2 + x1*x8
0
3
4
X3*X22 + X3*X4
Defining x4
x4
Defining x4
Defining x22
Defining x1, x2, x8
-2*x1*x2*x8 + x1*x2 + x1*x8
0
3
5
X3*X23 + X3*X5
Defining x5
x5
Defining x5
Defining x23
Defining x1, x2, x8
-2*x1*x2*x8 + x1*x2 + x1*x8
0
4
5
X4*X29 + X4*X5
Defining x5
x5
Defining x5
Defining x29
Defining x1, x2, x8
-2*x1*x2*x8 + x1*x2 + x1*x8
1
2
3
X8*X15 + X8*X9
Defining x9
x9
Defining x9
Defining x15
Defining x1, x2, x8
-2*x1*x2*x8 + x1*x2 + x1*x8
1
2
4
X8*X16 + X8*X10
Defining x10
x10
Defining x10
Defining x16
Defining x1, x2, x8
-2*x1*x2*x8 + x1*x2 + x1*x8
1
2
5
X8*X17 + X8*X11
Defining x11
x11
Defining x11
Defining x17
Defining x1, x2, x8
-2*x1*x2*x8 + x1*x2 + x1*x8
1
3
4
X9*X22 + X9*X10
Defining x10
x10
Defining x10
Defining x22
Defining x1, x2, x8
-2*x1*x2*x8 + x1*x2 + x1*x8
1
3
5
X9*X23 + X9*X11
Defining x11
x11
Defining x11
Defining x23
Defining x1, x2, x8
-2*x1*x2*x8 + x1*x2 + x1*x8
1
4
5
X10*X29 + X10*X11
Defining x11
x11
Defining x11
Defining x29
Defining x1, x2, x8
-2*x1*x2*x8 + x1*x2 + x1*x8
2
3
4
X15*X22 + X15*X16
Defining x16
x16
Defining x16
Defining x22
Defining x1, x2, x8
-2*x1*x2*x8 + x1*x2 + x1*x8
2
3
5
X15*X23 + X15*X17
Defining x17
x17
Defining x17
Defining x23
Defining x1, x2, x8
-2*x1*x2*x8 + x1*x2 + x1*x8
2
4
5
X16*X29 + X16*X17
Defining x17
x17
Defining x17
Defining x29
Defining x1, x2, x8
-2*x1*x2*x8 + x1*x2 + x1*x8
3
4
5
X22*X29 + X22*X23
Defining x23
x23
Defining x23
Defining x29
Defining x1, x2, x8
-2*x1*x2*x8 + x1*x2 + x1*x8
Defining x1, x2, x8
-2*x1*x2*x8 + x1*x8 + x1*x2
Defining x1, x2, x8
-2*x1*x2*x8 + x1*x8 + x1*x2
Defining x1, x2, x8
[x1*x2*x8, x1*x8, x1*x2]
(X1, X2, X8)
Defining x1, x2, x8
x1*x2*x8 + x2*x8 + x1*x8 + x8 + x1*x2 + x2 + x1 + 1
[x1*x2*x8, x2*x8, x1*x8, x8, x1*x2, x2, x1, 1]
(-2, 0, 1, 0, 1, 0, 0, 0)
-2*x1*x2*x8 + x1*x8 + x1*x2
Defining x1, x2, x8
-2*x1*x2*x8 + x2*x8 + x1*x8
Defining x1, x2, x8
-2*x1*x2*x8 + x2*x8 + x1*x2
Defining x1, x2, x8
-2*x1*x2*x8 + x2*x8 + x1*x2
Defining x1, x2
x1*x2 - x1 + 1
Defining x1, x2
x1*x2 - x1 + 1
objects = 12
Defining X0, X1, X2, X3, X4, X5, X6, X7, X8, X9, X10, X11, X12, X13, X14, X15, X16, X17, X18, X19, X20, X21, X22, X23, X24, X25, X26, X27, X28, X29, X30, X31, X32, X33, X34, X35, X36, X37, X38, X39, X40, X41, X42, X43, X44, X45, X46, X47
[1 0 0 0|0 1 0 0|0 0 0 1]
[0 1 0 0|0 0 0 1|1 0 0 0]
[0 0 1 0|1 0 0 0|0 0 1 0]
[0 0 0 1|0 0 1 0|0 1 0 0]
[-------+-------+-------]
[0 0 1 0|1 0 0 0|0 0 1 0]
[1 0 0 0|0 1 0 0|0 0 0 1]
[0 0 0 1|0 0 1 0|0 1 0 0]
[0 1 0 0|0 0 0 1|1 0 0 0]
[-------+-------+-------]
[0 1 0 0|0 0 0 1|1 0 0 0]
[0 0 0 1|0 0 1 0|0 1 0 0]
[0 0 1 0|1 0 0 0|0 0 1 0]
[1 0 0 0|0 1 0 0|0 0 0 1]
objects = 12
types = 3
rel_classes = 4
144 Free Boolean Algebra generators: X0 = R[0,0], X1 = R[0,1], X2 = R[0,2],..., X143 = R[11,11]
REI.gens() = 1589
A 1st pass
type 0 to type 1
[ X138 X124 + X126 + X128 0 X90 + X115 + X139]
[ X49 X61 0 X85]
[ X138 + 1 X124 + X125 + X126 + X129 + 1 X124 + X129 + 1 X88 + X90 + X115]
[ X51 X63 X75 X87]
type 0 to type 2
[ X138 + X140 X138 X126 + X129 + X142 X138 + 1]
[ X97 X138 X121 X133]
[X124 + X126 + X128 + X129 + 1 X124 + X129 + X138 + 1 X124 + X126 + X129 X138]
[ X99 X111 X123 X135]
type 1 to type 2
[X124 + X126 + X128 + X129 + X138 + 1 X124 + X129 + 1 X124 0]
[ X101 X125 + X129 + X137 + 1 X125 X137]
[ X116 + X138 X138 + 1 X126 X138]
[ X103 X115 X127 X139]
number of variables left to be determined: 31
REI.gens() = 1613
A 2nd pass
type 0 to type 1
[0 1 0 0]
[0 0 0 1]
[1 0 0 0]
[0 0 1 0]
type 0 to type 2
[0 0 0 1]
[1 0 0 0]
[0 0 1 0]
[0 1 0 0]
type 1 to type 2
[0 0 1 0]
[0 0 0 1]
[0 1 0 0]
[1 0 0 0]
objects = 24
types = 4
rel_classes = 6
576 Free Boolean Algebra generators: X0 = R[0,0], X1 = R[0,1], X2 = R[0,2],..., X575 = R[23,23]
REI.gens() = 13413
A 1st pass
type 0 to type 1
[ 0 X7 X7 + 1 0 0 0]
[ X30 X31 0 0 0 0]
[ X54 X55 X56 X57 X58 0]
[ 0 X79 X80 0 X82 0]
[ X102 X103 X104 X105 X106 0]
[ 0 0 0 0 0 1]
type 0 to type 2
[ X12 X13 X14 X15 0 X17]
[ 0 0 0 0 1 0]
[ X60 X61 X62 X63 0 X65]
[ X84 0 0 0 0 X89]
[X108 X109 X110 0 0 X113]
[X132 X133 X134 X135 0 X137]
type 0 to type 3
[ X18 0 X13 0 0 X23]
[ 0 0 X30 + 1 X30 0 0]
[ X66 X67 X68 X54 0 X71]
[X30 + 1 X30 0 0 0 0]
[ X114 X115 X116 X102 0 0]
[ 0 0 0 0 1 0]
type 1 to type 2
[ 0 X30 + 1 0 0 X30 0]
[ X180 X181 X182 X183 X31 X185]
[ X204 X205 0 X207 0 0]
[ X228 0 0 0 0 0]
[ X252 0 0 X255 0 0]
[ X132 X133 X134 X135 0 X137]
type 1 to type 3
[ 0 0 0 1 0 0]
[ X186 X187 X181 + X31 0 0 X191]
[ X210 X211 X205 0 0 X215]
[X133 + X30 X30 + 1 X133 0 0 0]
[ X258 X259 0 0 0 X263]
[ 0 0 0 0 1 0]
type 2 to type 3
[ X306 X307 X308 0 X132 X311]
[ 0 0 X133 + X30 X30 + 1 X133 0]
[ X354 0 0 0 X134 X359]
[ 0 0 0 0 X135 X135 + 1]
[ 0 0 X30 + 1 X30 0 0]
[ X426 X427 0 0 X137 X431]
number of variables left to be determined: 75
REI.gens() = 13463
A 2nd pass
type 0 to type 1
[0 0 1 0 0 0]
[1 0 0 0 0 0]
[0 0 0 0 1 0]
[0 1 0 0 0 0]
[0 0 0 1 0 0]
[0 0 0 0 0 1]
type 0 to type 2
[0 1 0 0 0 0]
[0 0 0 0 1 0]
[0 0 0 1 0 0]
[0 0 0 0 0 1]
[1 0 0 0 0 0]
[0 0 1 0 0 0]
type 0 to type 3
[0 0 1 0 0 0]
[0 0 0 1 0 0]
[0 0 0 0 0 1]
[0 1 0 0 0 0]
[1 0 0 0 0 0]
[0 0 0 0 1 0]
type 1 to type 2
[0 0 0 0 1 0]
[0 0 0 0 0 1]
[0 1 0 0 0 0]
[1 0 0 0 0 0]
[0 0 0 1 0 0]
[0 0 1 0 0 0]
type 1 to type 3
[0 0 0 1 0 0]
[0 1 0 0 0 0]
[0 0 1 0 0 0]
[1 0 0 0 0 0]
[0 0 0 0 0 1]
[0 0 0 0 1 0]
type 2 to type 3
[1 0 0 0 0 0]
[0 0 1 0 0 0]
[0 0 0 0 1 0]
[0 0 0 0 0 1]
[0 0 0 1 0 0]
[0 1 0 0 0 0]
percolation
[0 1 1 1 1]
[1 0 1 0 0]
[1 1 0 1 1]
[1 0 1 0 1]
[1 0 1 1 0]
[4 1 3 2 2]
[1 2 1 2 2]
[3 1 4 2 2]
[2 2 2 3 2]
[2 2 2 2 3]
[8 7 9 9 9]
[7 2 7 4 4]
[9 7 8 9 9]
[9 4 9 6 7]
[9 4 9 7 6]
[34 17 33 26 26]
[17 14 17 18 18]
[33 17 34 26 26]
[26 18 26 25 24]
[26 18 26 24 25]
Number of Shortest Paths
[0 1 1 1 1]
[1 0 1 2 2]
[1 1 0 1 1]
[1 2 1 0 1]
[1 2 1 1 0]
Shortest Path Length
[0 1 1 1 1]
[1 0 1 2 2]
[1 1 0 1 1]
[1 2 1 0 1]
[1 2 1 1 0]
[0 1 2 1 1 1 1 1 1 1 2 0]
[0 1 3 1 1 1 1 2 2 2 3 0]
[0 1 4 1 1 1 1 2 2 2 3 0]
[0 2 1 1 1 1 1 1 1 1 2 0]
[0 2 3 1 1 1 1 1 1 1 2 0]
[0 2 4 1 1 1 1 1 1 1 2 0]
[0 3 1 1 1 1 1 2 2 2 3 0]
[0 3 2 1 1 1 1 1 1 1 2 0]
[0 3 4 1 1 1 1 1 1 1 2 0]
[0 4 1 1 1 1 1 2 2 2 3 0]
[0 4 2 1 1 1 1 1 1 1 2 0]
[0 4 3 1 1 1 1 1 1 1 2 0]
[1 0 2 1 1 1 1 1 1 1 2 0]
[1 0 3 2 2 1 1 1 1 1 2 1]
[1 0 4 2 2 1 1 1 1 1 2 1]
[1 2 0 1 1 1 1 1 1 1 2 0]
[1 2 3 2 2 1 1 1 1 1 2 1]
[1 2 4 2 2 1 1 1 1 1 2 1]
[1 3 0 1 1 2 2 1 1 2 3 0]
[1 3 2 1 1 2 2 1 1 2 3 0]
[1 3 4 2 2 2 2 1 1 2 3 0]
[1 4 0 1 1 2 2 1 1 2 3 0]
[1 4 2 1 1 2 2 1 1 2 3 0]
[1 4 3 2 2 2 2 1 1 2 3 0]
[2 0 1 1 1 1 1 1 1 1 2 0]
[2 0 3 1 1 1 1 1 1 1 2 0]
[2 0 4 1 1 1 1 1 1 1 2 0]
[2 1 0 1 1 1 1 1 1 1 2 0]
[2 1 3 1 1 1 1 2 2 2 3 0]
[2 1 4 1 1 1 1 2 2 2 3 0]
[2 3 0 1 1 1 1 1 1 1 2 0]
[2 3 1 1 1 1 1 2 2 2 3 0]
[2 3 4 1 1 1 1 1 1 1 2 0]
[2 4 0 1 1 1 1 1 1 1 2 0]
[2 4 1 1 1 1 1 2 2 2 3 0]
[2 4 3 1 1 1 1 1 1 1 2 0]
[3 0 1 2 2 1 1 1 1 1 2 1]
[3 0 2 1 1 1 1 1 1 1 2 0]
[3 0 4 1 1 1 1 1 1 1 2 0]
[3 1 0 1 1 2 2 1 1 2 3 0]
[3 1 2 1 1 2 2 1 1 2 3 0]
[3 1 4 1 1 2 2 2 2 4 4 0]
[3 2 0 1 1 1 1 1 1 1 2 0]
[3 2 1 2 2 1 1 1 1 1 2 1]
[3 2 4 1 1 1 1 1 1 1 2 0]
[3 4 0 1 1 1 1 1 1 1 2 0]
[3 4 1 2 2 1 1 2 2 2 3 0]
[3 4 2 1 1 1 1 1 1 1 2 0]
[4 0 1 2 2 1 1 1 1 1 2 1]
[4 0 2 1 1 1 1 1 1 1 2 0]
[4 0 3 1 1 1 1 1 1 1 2 0]
[4 1 0 1 1 2 2 1 1 2 3 0]
[4 1 2 1 1 2 2 1 1 2 3 0]
[4 1 3 1 1 2 2 2 2 4 4 0]
[4 2 0 1 1 1 1 1 1 1 2 0]
[4 2 1 2 2 1 1 1 1 1 2 1]
[4 2 3 1 1 1 1 1 1 1 2 0]
[4 3 0 1 1 1 1 1 1 1 2 0]
[4 3 1 2 2 1 1 2 2 2 3 0]
[4 3 2 1 1 1 1 1 1 1 2 0]
60
[0 1 2 1 1 0]
[0 1 3 1 1 0]
[0 1 4 1 1 0]
[0 2 1 1 1 0]
[0 2 3 1 1 0]
[0 2 4 1 1 0]
[0 3 1 1 1 0]
[0 3 2 1 1 0]
[0 3 4 1 1 0]
[0 4 1 1 1 0]
[0 4 2 1 1 0]
[0 4 3 1 1 0]
[1 0 2 1 1 0]
[1 0 3 2 2 1]
[1 0 4 2 2 1]
[1 2 0 1 1 0]
[1 2 3 2 2 1]
[1 2 4 2 2 1]
[1 3 0 1 1 0]
[1 3 2 1 1 0]
[1 3 4 2 2 1]
[1 4 0 1 1 0]
[1 4 2 1 1 0]
[1 4 3 2 2 1]
[2 0 1 1 1 0]
[2 0 3 1 1 0]
[2 0 4 1 1 0]
[2 1 0 1 1 0]
[2 1 3 1 1 0]
[2 1 4 1 1 0]
[2 3 0 1 1 0]
[2 3 1 1 1 0]
[2 3 4 1 1 0]
[2 4 0 1 1 0]
[2 4 1 1 1 0]
[2 4 3 1 1 0]
[3 0 1 2 2 1]
[3 0 2 1 1 0]
[3 0 4 1 1 0]
[3 1 0 1 1 0]
[3 1 2 1 1 0]
[3 1 4 1 1 0]
[3 2 0 1 1 0]
[3 2 1 2 2 1]
[3 2 4 1 1 0]
[3 4 0 1 1 0]
[3 4 1 2 2 1]
[3 4 2 1 1 0]
[4 0 1 2 2 1]
[4 0 2 1 1 0]
[4 0 3 1 1 0]
[4 1 0 1 1 0]
[4 1 2 1 1 0]
[4 1 3 1 1 0]
[4 2 0 1 1 0]
[4 2 1 2 2 1]
[4 2 3 1 1 0]
[4 3 0 1 1 0]
[4 3 1 2 2 1]
[4 3 2 1 1 0]
Defining x1, x2, x8
-2*x1*x2*x8 + x1*x8 + x1*x2
Defining x1, x2, x8
-2*x1*x2*x8 + x1*x8 + x1*x2