

last edited 6 years ago by test1 
1 2  
Editor: test1
Time: 2018/02/17 15:53:14 GMT+0 

Note: 
changed: variable in Axiom by the command variable in FriCAS by the command changed: is a frequent expectation of new users of Axiom  especially if one has used other computer algebra systems, after all Axiom is supposed is a frequent expectation of new users of FriCAS  especially if one has used other computer algebra systems, after all FriCAS is supposed changed: Unfortunately Axiom does not attempt to use this type information Unfortunately FriCAS does not attempt to use this type information changed: When you write 'n:PositiveInteger' what this tells Axiom is that When you write 'n:PositiveInteger' what this tells FriCAS is that changed: To me, this is a tremedous waste of an opportunity in Axiom to To me, this is a tremedous waste of an opportunity in FriCAS to
The idea that one should be able to "declare the type" of a variable in FriCAS by the command
n:PositiveInteger
is a frequent expectation of new users of FriCAS  especially if one has used other computer algebra systems, after all FriCAS is supposed to be a "strongly typed" system, right?
Unfortunately FriCAS does not attempt to use this type information when forming expressions  but worse  declaring the type actually interferes with the use of the variable to form expressions!
n+1
n is declared as being in PositiveInteger but has not been given a value.
When you write n:PositiveInteger
what this tells FriCAS is that
n
will be assigned an integer value greater than 0  only that.
After it is actually assigned some value, then it can be used
exactly like that value, but not before.
To me, this is a tremedous waste of an opportunity in FriCAS to to deal with "domain of computation" issues such as are addressed in other untyped computer algebra systems by the use of "assumptions" such as:
assume(x,PositiveInteger);
Such knowledge can be used to considerably improve the quality and generality of the computations.
There was plenty of discussion on axiomdeveloper, but no concensus yet, I'm afraid. Here are some of the related threads:
See also The Unknown In Computer Algebra
The Unknown In Computer Algebra
)abbrev domain PUNINT PureUnknownInteger PureUnknownInteger (D,BasicUnknown):Ring == Implementation where D:IntegerNumberSystem BasicUnknown:List Symbol Implementation ==> LocalAlgebra (Polynomial D, D, D) with "/" : ($, D) > $ ++ a/n computes the expression whose value is a/n if it ++ is actually an unknown integer
Compiling FriCAS source code from file /var/lib/zope2.10/instance/axiomwiki/var/LatexWiki/734945227110916105725px003.spad using old system compiler. PUNINT abbreviates domain PureUnknownInteger ******** Spad syntax error detected ******** Expected: ) The prior line was:
5> Implementation ==> LocalAlgebra (Polynomial D,D, D) with
The current line is:
6> "/" : ($,D) > $
The number of valid tokens is 1. The prior token was #S(TOKEN :SYMBOL ( :TYPE KEYWORD :NONBLANK NIL :LINE_NUM 6 :CHAR_NUM 10) The current token is #S(TOKEN :SYMBOL $ :TYPE KEYWORD :NONBLANK NIL :LINE_NUM 6 :CHAR_NUM 11)