Wed Apr 16 20:15:32 MET DST 1997 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 -- ---------- Mathematics vs Computer Science ---------- -- Is k really treated as a local variable in the following situations where it -- is clearly a mathematically local variable? sum(k, k = 1..4) (1) 10 Type: Fraction Polynomial Integer Time: 0.13 (IN) + 0.32 (EV) + 0.12 (OT) + 0.15 (GC) = 0.72 sec product(k, k = 1..3) (2) 6 Type: Expression Integer Time: 0.55 (IN) + 0.13 (EV) + 0.17 (OT) + 0.07 (GC) = 0.92 sec limit(k, k = 0) (3) 0 Type: Union(OrderedCompletion Expression Integer,...) Time: 0.33 (IN) + 0.10 (EV) + 0.02 (OT) + 0.05 (GC) = 0.50 sec integrate(k, k = 0..1) 1 (4) - 2 Type: Union(f1: OrderedCompletion Expression Integer,...) Time: 0.12 (IN) + 0.43 (EV) + 0.02 (OT) + 0.03 (GC) = 0.60 sec k:= 1; Type: PositiveInteger Time: 0.02 (IN) = 0.02 sec sum(k, k = 1..4) There are 6 exposed and 2 unexposed library operations named sum having 2 argument(s) but none was determined to be applicable. Use HyperDoc Browse, or issue )display op sum 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 sum with argument type(s) PositiveInteger Equation Segment PositiveInteger product(k, k = 1..3) There are 4 exposed and 2 unexposed library operations named product having 2 argument(s) but none was determined to be applicable. Use HyperDoc Browse, or issue )display op product 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 product with argument type(s) PositiveInteger Equation Segment PositiveInteger limit(k, k = 0) >> Error detected within library code: limit:left hand side must be a variable initial (6) -> real 14.4 user 4.8 sys 0.4 ------------------------------------------------------------------------------- Wed Apr 16 20:28:26 MET DST 1997 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 -- ---------- Mathematics vs Computer Science ---------- -- Is k really treated as a local variable in the following situations where it -- is clearly a mathematically local variable? k:= 1; Type: PositiveInteger Time: 0 sec integrate(k, k = 0..1) There are 11 exposed and 7 unexposed library operations named integrate having 2 argument(s) but none was determined to be applicable. Use HyperDoc Browse, or issue )display op integrate 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 integrate with argument type(s) PositiveInteger Equation Segment NonNegativeInteger -- ---------- Quit ---------- )quit real 5.6 user 2.1 sys 0.2