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