axiom-test 20120501-8 / usr / share / axiom-20120501 / input / allfact.input

This file is indexed.

/usr/share/axiom-20120501/input/allfact.input is in axiom-test 20120501-8.

This file is owned by root:root, with mode 0o644.

The actual contents of the file can be viewed below. 

  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
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
)set break resume
)spool allfact.output
)set message test on
)set message auto off
)clear all
-- factorization of integer numbers
--S 1 of 21
n:=45234258258293
--R 
--R
--R   (1)  45234258258293
--R                                                        Type: PositiveInteger
--E 1

--S 2 of 21
factor n
--R 
--R
--R   (2)  13 19 269 8387 81173
--R                                                      Type: Factored(Integer)
--E 2

-- factorization of gaussian integers
--S 3 of 21
m:(Complex Integer) := 1324567+%i*53523582
--R 
--R
--R   (3)  1324567 + 53523582%i
--R                                                       Type: Complex(Integer)
--E 3

--S 4 of 21
factor m
--R 
--R
--R   (4)  (2 + 7%i)(7119136 + 1844815%i)
--R                                             Type: Factored(Complex(Integer))
--E 4

-- factorization of polynomials over finite fields
--S 5 of 21
u:UP(x,PF(19)) :=3*x**4+2*x**2+15*x+18
--R 
--R
--R          4     2
--R   (5)  3x  + 2x  + 15x + 18
--R                                 Type: UnivariatePolynomial(x,PrimeField(19))
--E 5

--S 6 of 21
factor u
--R 
--R
--R                   3    2
--R   (6)  3(x + 18)(x  + x  + 8x + 13)
--R                       Type: Factored(UnivariatePolynomial(x,PrimeField(19)))
--E 6

-- factorization of polynomials over the integers
--S 7 of 21
v:UP(x,INT):= (4*x**3+2*x**2+1)*(12*x**5-x**3+12)
--R 
--R
--R           8      7     6      5      3      2
--R   (7)  48x  + 24x  - 4x  + 10x  + 47x  + 24x  + 12
--R                                        Type: UnivariatePolynomial(x,Integer)
--E 7

--S 8 of 21
factor v
--R 
--R
--R           3     2         5    3
--R   (8)  (4x  + 2x  + 1)(12x  - x  + 12)
--R                              Type: Factored(UnivariatePolynomial(x,Integer))
--E 8

-- factorization of multivariate polynomial over the integers
--S 9 of 21
w:MPOLY([x,y,z],INT) :=(x**2-y**2-z**2)*(x**2+y**2+z**2)*(z*y+3*z)
--R 
--R
--R                   4      5       4     3 3     3 2    5      5
--R   (9)  (z y + 3z)x  - z y  - 3z y  - 2z y  - 6z y  - z y - 3z
--R                                Type: MultivariatePolynomial([x,y,z],Integer)
--E 9

--S 10 of 21
factor w
--R 
--R
--R                   2    2    2   2    2    2
--R   (10)  z(y + 3)(x  - y  - z )(x  + y  + z )
--R                      Type: Factored(MultivariatePolynomial([x,y,z],Integer))
--E 10

-- factorization of univariate and multivariate over the rational numbers
--S 11 of 21
f:MPOLY([x,y,z],FRAC INT) :=(4/9*x**2-1/16)*(x**3/27+125)
--R 
--R
--R          4   5    1   3   500  2   125
--R   (11)  --- x  - --- x  + --- x  - ---
--R         243      432       9        16
--R                      Type: MultivariatePolynomial([x,y,z],Fraction(Integer))
--E 11

--S 12 of 21
factor f
--R 
--R
--R          4       3      3           2
--R   (12)  --- (x - -)(x + -)(x + 15)(x  - 15x + 225)
--R         243      8      8
--R            Type: Factored(MultivariatePolynomial([x,y,z],Fraction(Integer)))
--E 12

-- factorization over rational functions
--S 13 of 21
g:DMP([x,y],FRAC POLY INT):=a**2*x**2/b**2 -c**2*y**2/d**2
--R 
--R
--R          2       2
--R         a   2   c   2
--R   (13)  -- x  - -- y
--R          2       2
--R         b       d
--R Type: DistributedMultivariatePolynomial([x,y],Fraction(Polynomial(Integer)))
--E 13

--S 14 of 21
factor g
--R 
--R
--R          2
--R         a       b c        b c
--R   (14)  -- (x - --- y)(x + --- y)
--R          2      a d        a d
--R         b
--IType: Factored ...
--E 14

-- decomposition of a rational function
--S 15 of 21
r:FRAC POLY INT:= (a**3/b**3-c**3/(b+1)**3)*(a*d+a/c)
--R 
--R
--R   (15)
--R         3 4     4 3     4 2     4     4          3 3    4 3     4 2     4     4
--R   (- a b c  + (a b  + 3a b  + 3a b + a )c)d - a b c  + a b  + 3a b  + 3a b + a
--R   -----------------------------------------------------------------------------
--R                                 6     5     4    3
--R                               (b  + 3b  + 3b  + b )c
--R                                          Type: Fraction(Polynomial(Integer))
--E 15

--S 16 of 21
factorFraction r
--R 
--R
--R                             2 2       2            2 2     2     2
--R           a(b c - a b - a)(b c  + (a b  + a b)c + a b  + 2a b + a )(c d + 1)
--R   (16)  - ------------------------------------------------------------------
--R                                        3       3
--R                                       b (b + 1) c
--R                                Type: Fraction(Factored(Polynomial(Integer)))
--E 16

-- factorization over simple algebraic extensions
--S 17 of 21
aa|aa**2+aa+1
--R 
--R   Your statement has resulted in the following assignments and 
--R      declaration:
--R
--I   SAEaa := SimpleAlgebraicExtension(Fraction Integer,...
--R   aa : SAEaa := aa
--R
--R   (17)  aa
--IType: SimpleAlgebraicExtension(Fraction Integer,...
--E 17

--S 18 of 21
p:UP(x,SAEaa) :=(x**3+aa**2*x+1)*(aa*x**2+aa*x+aa)**2
--R 
--R
--R   (18)
--R                7               6               5              4     3
--R     (- aa - 1)x  + (- 2aa - 2)x  + (- 2aa - 3)x  + (- aa - 3)x  - 3x
--R   + 
--R                2
--R     (- aa - 3)x  + (- aa - 2)x - aa - 1
--IType: UnivariatePolynomial(x,SimpleAlgebraicExtension(...
--E 18

--S 19 of 21
factor(p)$SAEFACT(UP('aa,FRAC INT),SAEaa,UP(x,SAEaa))
--R 
--R
--R                           2            2  3
--R   (19)  (- aa - 1)(x - aa) (x + aa + 1) (x  + (- aa - 1)x + 1)
--IType: Factored UnivariatePolynomial(x,SimpleAlgebraicExtension(...
--E 19

-- factorization over algebraic numbers
--S 20 of 21
a:=rootOf(a**2+3)$AN
--R 
--R
--R   (20)  a
--R                                                        Type: AlgebraicNumber
--E 20

--S 21 of 21
factor(x**2+x+1,[a])
--R 
--R
--R              - a + 1      a + 1
--R   (21)  (x + -------)(x + -----)
--R                 2           2
--R                                  Type: Factored(Polynomial(AlgebraicNumber))
--E 21
)spool
)lisp (bye)

APT Browse - Built by Thomas Orozco.