/usr/lib/open-axiom/input/ruleset.input is in open-axiom-test 1.5.0~svn3056+ds-1.
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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 | --Copyright The Numerical Algorithms Group Limited 1991.
)cl all
-- This is the example from "Programming in Mathematica", p.139
TrigLinearRules := rule
sin(x) * sin(y) == cos(x-y)/2 - cos(x+y)/2
cos(x) * cos(y) == cos(x+y)/2 + cos(x-y)/2
sin(x) * cos(y) == sin(x+y)/2 + sin(x-y)/2
sin(x)**(n | integer? n and n > 0) == (1-cos(2*x))/2 * sin(x)**(n-2)
cos(x)**(n | integer? n and n > 0) == (1+cos(2*x))/2 * cos(x)**(n-2)
sin(a)*cos(b) + sin(a)*cos(a) + cos(2*a)*cos(3*a)
TrigLinearRules %
sin(a) * sin(2*a) * sin(3*a) * sin(4*a)
TrigLinearRules %
-- Defining an operator to be linear w.r.t. its 2nd argument
f := operator 'f
FLinearRules := rule
f(a + b, x) == f(a, x) + f(b, x)
f(c * a, x | freeOf?(c, x)) == c * f(a, x)
f(2*x + a * log(x) + x * log(x), x)
FLinearRules %
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