/usr/lib/open-axiom/input/genups.input is in open-axiom-test 1.5.0~svn3056+ds-1.
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 | --Copyright The Numerical Algorithms Group Limited 1991.
)cl all
taylor(n +-> 1/factorial(n),x = 0) -- expansion of exp(x) at x = 0
taylor(n +-> (-1)**(n-1)/n,x = 1,1..) -- expansion of log(x) at x = 1
taylor(n +-> (-1)**(n-1)/n,x = 1,1..6) -- truncated expansion of log(x)
laurent(m +-> m**2,x = 7,-2..) -- infinite Laurent expansion
laurent(m +-> m**2,x = 7,-2..5) -- finite Laurent expansion
puiseux(i +-> (-1)**((i-1)/2)/factorial(i),x = 0,1..,2) -- sin(x) at x = 0
puiseux(i +-> (-1)**(i/2)/factorial(i),x = 0,0..,2) -- cos(x) at x = 0
-- puiseux(i +-> (-1)**((i-1)/2)/factorial(i),x = 0,1..9,2) -- truncated sin(x)
-- interpretor needs help here
puiseux(i +-> (-1)**((i-1)/2)/factorial(i),x = 0,1..9/1,2) -- truncated sin(x)
puiseux(j +-> j,x = 8,-4/3..,1/2)
puiseux(j +-> j,x = 8,-4/3..1/6,1/2)
-- same computations using expressions instead of functions
taylor(1/factorial(n),n,x = 0) -- expansion of exp(x) at x = 0
taylor((-1)**(n-1)/n,n,x = 1,1..) -- expansion of log(x) at x = 1
taylor((-1)**(n-1)/n,n,x = 1,1..6) -- truncated expansion of log(x)
laurent(m**2,m,x = 7,-2..) -- infinite Laurent expansion
laurent(m**2,m,x = 7,-2..5) -- finite Laurent expansion
puiseux((-1)**((i-1)/2)/factorial(i),i,x = 0,1..,2) -- sin(x) at x = 0
puiseux((-1)**(i/2)/factorial(i),i,x = 0,0..,2) -- cos(x) at x = 0
-- puiseux((-1)**((i-1)/2)/factorial(i),i,x = 0,1..9,2) -- truncated sin(x)
-- interpretor needs help here
puiseux((-1)**((i-1)/2)/factorial(i),i,x = 0,1..9/1,2) -- truncated sin(x)
puiseux(j,j,x = 8,-4/3..,1/2)
puiseux(j,j,x = 8,-4/3..1/6,1/2)
-- all of the above commands should still work when the functions 'taylor',
-- 'laurent', and 'puiseux' are replaced by 'series':
series(n +-> 1/factorial(n),x = 0) -- expansion of exp(x) at x = 0
series(n +-> (-1)**(n-1)/n,x = 1,1..) -- expansion of log(x) at x = 1
series(n +-> (-1)**(n-1)/n,x = 1,1..6) -- truncated expansion of log(x)
series(m +-> m**2,x = 7,-2..) -- infinite Laurent expansion
series(m +-> m**2,x = 7,-2..5) -- finite Laurent expansion
series(i +-> (-1)**((i-1)/2)/factorial(i),x = 0,1..,2) -- sin(x) at x = 0
series(i +-> (-1)**(i/2)/factorial(i),x = 0,0..,2) -- cos(x) at x = 0
-- series(i +-> (-1)**((i-1)/2)/factorial(i),x = 0,1..9,2) -- truncated sin(x)
-- interpretor needs help here
series(i +-> (-1)**((i-1)/2)/factorial(i),x = 0,1..9/1,2) -- truncated sin(x)
series(j +-> j,x = 8,-4/3..,1/2)
series(j +-> j,x = 8,-4/3..1/6,1/2)
-- same computations using expressions instead of functions
series(1/factorial(n),n,x = 0) -- expansion of exp(x) at x = 0
series((-1)**(n-1)/n,n,x = 1,1..) -- expansion of log(x) at x = 1
series((-1)**(n-1)/n,n,x = 1,1..6) -- truncated expansion of log(x)
series(m**2,m,x = 7,-2..) -- infinite Laurent expansion
series(m**2,m,x = 7,-2..5) -- finite Laurent expansion
series((-1)**((i-1)/2)/factorial(i),i,x = 0,1..,2) -- sin(x) at x = 0
series((-1)**(i/2)/factorial(i),i,x = 0,0..,2) -- cos(x) at x = 0
-- series((-1)**((i-1)/2)/factorial(i),i,x = 0,1..9,2) -- truncated sin(x)
-- interpretor needs help here
series((-1)**((i-1)/2)/factorial(i),i,x = 0,1..9/1,2) -- truncated sin(x)
series(j,j,x = 8,-4/3..,1/2)
series(j,j,x = 8,-4/3..1/6,1/2)
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