/usr/share/axiom-20120501/input/davenport.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 | )set break resume
)sys rm -f davenport.output
)spool davenport.output
)set message test on
)set message auto off
)clear all
--S 1 of 12
t1:=UP(x,FRAC INT)
--R
--R
--R (1) UnivariatePolynomial(x,Fraction(Integer))
--R Type: Domain
--E 1
--S 2 of 12
quotient(p1:t1,p2:t1,n:NNI):Union("failed",t1) ==
minimumDegree(p1) < minimumDegree(p2) => "failed"
reste:UP(x,FRAC INT):=p1
degp2:=minimumDegree(p2)
coefp2:=coefficient(p2,degp2)
quot:UP(x,FRAC INT):=0
while degree(quot) < n repeat
deg:=minimumDegree(reste)
mon:=monomial(coefficient(reste,deg)/coefp2,deg-degp2)$UP(x,FRAC INT)
reste:=reste-(mon*p2)
quot:=quot+mon
quot
--R
--R Function declaration quotient : (UnivariatePolynomial(x,Fraction(
--R Integer)),UnivariatePolynomial(x,Fraction(Integer)),
--R NonNegativeInteger) -> Union("failed",UnivariatePolynomial(x,
--R Fraction(Integer))) has been added to workspace.
--R Type: Void
--E 2
--S 3 of 12
quotient(1,1+x,8)
--R
--R Your expression cannot be fully compiled because it contains an
--R integer expression (for - ) whose sign cannot be determined (in
--R general) and so must be specified by you. Perhaps you can try
--R substituting something like
--R (- :: PI)
--R or
--R (- :: NNI)
--R into your expression for - .
--R AXIOM will attempt to step through and interpret the code.
--R Compiling function quotient with type (UnivariatePolynomial(x,
--R Fraction(Integer)),UnivariatePolynomial(x,Fraction(Integer)),
--R NonNegativeInteger) -> Union("failed",UnivariatePolynomial(x,
--R Fraction(Integer)))
--I Compiling function G1504 with type Integer -> Boolean
--R
--R 8 7 6 5 4 3 2
--R (3) x - x + x - x + x - x + x - x + 1
--R Type: Union(UnivariatePolynomial(x,Fraction(Integer)),...)
--E 3
--S 4 of 12
quotient(x**2-x+1,x**3-x-6/7,8)
--R
--R
--R (4)
--R 84778967 8 18089477 7 2286095 6 166061 5 8281 4 4459 3
--R -------- x - -------- x + ------- x - ------ x - ---- x + ---- x
--R 10077696 1679616 279936 46656 7776 1296
--R +
--R 889 2 91 7
--R - --- x + -- x - -
--R 216 36 6
--R Type: Union(UnivariatePolynomial(x,Fraction(Integer)),...)
--E 4
--S 5 of 12
ext1:=SAE(FRAC INT,UP(a,FRAC INT),a**2+a+1)
--R
--R
--R (5)
--R SimpleAlgebraicExtension(Fraction(Integer),UnivariatePolynomial(a,Fraction(In
--R teger)),a^2+a+1)
--R Type: Domain
--E 5
--S 6 of 12
e:ext1:=convert(((3/4)*a**2-a+(7/4))::UP(a,FRAC INT))
--R
--R
--R 7
--R (6) - - a + 1
--R 4
--IType: SimpleAlgebraicExtension(Fraction Integer,...
--E 6
--S 7 of 12
recip(e)
--R
--R
--R 28 44
--R (7) -- a + --
--R 93 93
--IType: Union(SimpleAlgebraicExtension(Fraction Integer,...
--E 7
--S 8 of 12
e**2
--R
--R
--R 105 33
--R (8) - --- a - --
--R 16 16
--IType: SimpleAlgebraicExtension(Fraction Integer,...
--E 8
--S 9 of 12
e:=convert((a**2-1)::UP(a,FRAC INT))
--R
--R
--R (9) - a - 2
--IType: SimpleAlgebraicExtension(Fraction Integer,...
--E 9
--S 10 of 12
p1:UP(x,ext1):=x**4+3*x**3+(2*a+1)*x**2+(3*a+3)*x-1
--R
--R
--R 4 3 2
--R (10) x + 3x + (2a + 1)x + (3a + 3)x - 1
--IType: UnivariatePolynomial(x,SimpleAlgebraicExtension(...
--E 10
--S 11 of 12
p2:UP(x,ext1):=x**2+a+1
--R
--R
--R 2
--R (11) x + a + 1
--IType: UnivariatePolynomial(x,SimpleAlgebraicExtension(...
--E 11
--S 12 of 12
p2/p1
--R
--R
--R 1
--R (12) -----------
--R 2
--R x + 3x + a
--IType: Fraction UnivariatePolynomial(x,SimpleAlgebraicExtension(...
--E 12
)spool
)lisp (bye)
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