Tue Jan 20 06:05:32 MET 1998 anne % axiom Axiom Computer Algebra System (Release 2.1) Digital Unix on DEC Alpha (AXIOM Sockets) The AXIOM server number is undefined. ----------------------------------------------------------------------------- Issue )copyright to view copyright notices. Issue )summary for a summary of useful system commands. Issue )quit to leave AXIOM and return to shell. ----------------------------------------------------------------------------- initial (1) -> -- ----------[ A x i o m ]---------- -- ---------- Initialization ---------- )set messages autoload off )set messages time on )set quit unprotected -- ---------- Inequalities ---------- -- => True %e**%pi > %pi**%e (1) false Type: Boolean Time: 0.30 (IN) + 0.38 (EV) + 0.18 (OT) + 0.15 (GC) = 1.02 sec -- => [True, False] [x**4 - x + 1 > 0, x**4 - x + 1 > 1] (2) [true,true] Type: List Boolean Time: 0.05 (IN) + 0.02 (EV) + 0.02 (OT) = 0.08 sec -- => True --assume(abs(x) < 1) -1 < x and x < 1 (3) false Type: Boolean Time: 0.23 (IN) + 0.02 (OT) = 0.25 sec -- x > y > 0 and k, n > 0 => k x^n > k y^n --assume(x > y, y > 0) 2*x**2 > 2*y**2 (4) false Type: Boolean Time: 0.02 (IN) + 0.02 (OT) = 0.03 sec --assume(k > 0) k*x**2 > k*y**2 (5) false Type: Boolean Time: 0.02 (EV) = 0.02 sec --assume(n > 0) k*x**n > k*y**n (6) false Type: Boolean Time: 0.18 (IN) + 0.03 (OT) = 0.22 sec -- x > 1 and y >= x - 1 => y > 0 --assume(x > 1, y >= x - 1) y > 0 (7) true Type: Boolean Time: 0.03 (IN) = 0.03 sec -- x >= y, y >= z, z >= x => x = y = z --assume(x >= y, y >= z, z >= x) [x = y, x = z, y = z] (8) [x= y,x= z,y= z] Type: List Equation Symbol Time: 0.13 (IN) + 0.02 (OT) = 0.15 sec -- x < -1 or x > 3 solve(abs(x - 1) > 2, x) There are 18 exposed and 3 unexposed library operations named solve having 2 argument(s) but none was determined to be applicable. Use HyperDoc Browse, or issue )display op solve to learn more about the available operations. Perhaps package-calling the operation or using coercions on the arguments will allow you to apply the operation. Cannot find a definition or applicable library operation named solve with argument type(s) Boolean Variable x -- x < 1 or 2 < x < 3 or 4 < x < 5 solve((x - 1)*(x - 2)*(x - 3)*(x - 4)*(x - 5) < 0, x) There are 18 exposed and 3 unexposed library operations named solve having 2 argument(s) but none was determined to be applicable. Use HyperDoc Browse, or issue )display op solve to learn more about the available operations. Perhaps package-calling the operation or using coercions on the arguments will allow you to apply the operation. Cannot find a definition or applicable library operation named solve with argument type(s) Boolean Variable x -- x < 3 or x >= 5 solve(6/(x - 3) <= 3, x) There are 18 exposed and 3 unexposed library operations named solve having 2 argument(s) but none was determined to be applicable. Use HyperDoc Browse, or issue )display op solve to learn more about the available operations. Perhaps package-calling the operation or using coercions on the arguments will allow you to apply the operation. Cannot find a definition or applicable library operation named solve with argument type(s) Boolean Variable x -- => 0 <= x < 4 solve(sqrt(x) < 2, x) There are 18 exposed and 3 unexposed library operations named solve having 2 argument(s) but none was determined to be applicable. Use HyperDoc Browse, or issue )display op solve to learn more about the available operations. Perhaps package-calling the operation or using coercions on the arguments will allow you to apply the operation. Cannot find a definition or applicable library operation named solve with argument type(s) Boolean Variable x -- => x is real solve(sin(x) < 2, x) There are 18 exposed and 3 unexposed library operations named solve having 2 argument(s) but none was determined to be applicable. Use HyperDoc Browse, or issue )display op solve to learn more about the available operations. Perhaps package-calling the operation or using coercions on the arguments will allow you to apply the operation. Cannot find a definition or applicable library operation named solve with argument type(s) Boolean Variable x -- => x != pi/2 + n 2 pi solve(sin(x) < 1, x) There are 18 exposed and 3 unexposed library operations named solve having 2 argument(s) but none was determined to be applicable. Use HyperDoc Browse, or issue )display op solve to learn more about the available operations. Perhaps package-calling the operation or using coercions on the arguments will allow you to apply the operation. Cannot find a definition or applicable library operation named solve with argument type(s) Boolean Variable x -- The next two examples come from Abdubrahim Muhammad Farhat, _Stability -- Analysis of Finite Difference Schemes_, Ph.D. dissertation, University of -- New Mexico, Albuquerque, New Mexico, December 1993 => 0 <= A <= 1/2 solve(abs(2*A*(cos(t) - 1) + 1) <= 1, A) There are 18 exposed and 3 unexposed library operations named solve having 2 argument(s) but none was determined to be applicable. Use HyperDoc Browse, or issue )display op solve to learn more about the available operations. Perhaps package-calling the operation or using coercions on the arguments will allow you to apply the operation. Cannot find a definition or applicable library operation named solve with argument type(s) Boolean Variable A -- => 125 A^4 + 24 A^2 - 48 < 0 or |A| < 2/5 sqrt([8 sqrt(6) - 3]/5) solve(A**2*(cos(t) - 4)**2*sin(t)**2 < 9, A) There are 18 exposed and 3 unexposed library operations named solve having 2 argument(s) but none was determined to be applicable. Use HyperDoc Browse, or issue )display op solve to learn more about the available operations. Perhaps package-calling the operation or using coercions on the arguments will allow you to apply the operation. Cannot find a definition or applicable library operation named solve with argument type(s) Boolean Variable A -- => |x| < y solve([x + y > 0, x - y < 0], [x, y]) There are 18 exposed and 3 unexposed library operations named solve having 2 argument(s) but none was determined to be applicable. Use HyperDoc Browse, or issue )display op solve to learn more about the available operations. Perhaps package-calling the operation or using coercions on the arguments will allow you to apply the operation. Cannot find a definition or applicable library operation named solve with argument type(s) List Boolean List OrderedVariableList [x,y] -- ---------- Quit ---------- )quit real 24.5 user 6.0 sys 0.4