rdp@teddy.UUCP (01/27/86)
I am looking for a program that can solve simple algebraic expressions
of the type:
10x - 15 = 5
(very simple stuff, eh?)
The idea is to have something that can solve, simplify or expand algebraic
formula that a beginning algebra student might encounter.
I would like to try to come up with a SIMPLE system that can demonstrate
the rules used to solve such equations, and possibly even coach a student.
Note that I am looking for simple solutions, I have no need of the extensive
capabilities of MACSYMA or some such thing.
A sample "session" might look something like:
Given:
10x - 15 = 5
Let's solve for x by adding 15 to both sides of the equation:
10x - 15 = 5
+15 = +15
______________
10x = 20
Now, we must eliminate the factor on x by dividing both sides
of the equation by 10:
10x = 20
___ __
10 10
This leaves:
x = 2
Now, along the way, the student might want to invoke something that explains
why something is being done. Does this necessarily imply a "rule-based" system?
(I, personally, expect not, but what do I know? :-)
Ths system would have the capability of SIMPLIFYING expressions, EXPANDING
expressions and SOLVING expressions (where possible).
Any help, pointers, suggestions, etc. from people is much appreciated.
Dick Piercecopp@petrus.UUCP (01/28/86)
Sounds like a nice project, Dick. Have fun!
mozetic@uiucdcsb.CS.UIUC.EDU (01/29/86)
Some work on algebraic manipulation was done at the Edinburgh Univ. (Dept. of AI) by A.Bundy and others. I can give you few references: Bundy, Silver: Preparing Equations for Change in Unknown, IJCAI-81, and DAI research paper 159. Bundy, Sterling: Meta-level Inference in Algebra, DAI 164. Bundy, Welham: Using Meta-level Inference for Selective Application of Multiple Rewrite Rules in Algebraic Manipulation, Artificial Intelligence 16(2), 1981. You may also consult the book: Bundy: The Computer Modelling of Mathematical Reasoning, Academic Press, 1983. Good luck.
dpb@philabs.UUCP (Paul Benjamin) (01/29/86)
> I am looking for a program that can solve simple algebraic expressions > of the type: > > 10x - 15 = 5 > > (very simple stuff, eh?) > ... > > Any help, pointers, suggestions, etc. from people is much appreciated. > > Dick Pierce You may want to look at Sleeman's work, although it is more along the lines of simulating student's solutions to such tasks. It can be found with related work in "Intelligent Tutoring Systems", published by Academic Press in 1982. The editors are D. Sleeman and J. S. Brown. Good luck. Paul Benjamin
gsmith@brahms.BERKELEY.EDU (Gene Ward Smith) (01/30/86)
>Note that I am looking for simple solutions, I have no need of the extensive >capabilities of MACSYMA or some such thing. > >Ths system would have the capability of SIMPLIFYING expressions, EXPANDING >expressions and SOLVING expressions (where possible). > >Dick Pierce Why NOT use MACSYMA? It already exists, and it does everything you want. Why not try it?
rdp@teddy.UUCP (01/30/86)
> >Note that I am looking for simple solutions, I have no need of the extensive > >capabilities of MACSYMA or some such thing. > > > >Ths system would have the capability of SIMPLIFYING expressions, EXPANDING > >expressions and SOLVING expressions (where possible). > > > >Dick Pierce > > > > Why NOT use MACSYMA? It already exists, and it does everything you want. > Why not try it? Several reasons, first of all, it needs to work on fairly small (pdp-11, non-unix) machines. Second, it's purpose is to act a a simple but patient tutor in pre-algebra. Consequently it must give hints, advice, etc. Thirdly, again, there is no need of all of MACSYMA. Dick Pierce
ladkin@kestrel.ARPA (01/31/86)
In article <11618@ucbvax.BERKELEY.EDU>, gsmith@brahms.BERKELEY.EDU (Gene Ward Smith) writes: > >Note that I am looking for simple solutions, I have no need of the extensive > >capabilities of MACSYMA or some such thing. > > > >Ths system would have the capability of SIMPLIFYING expressions, EXPANDING > >expressions and SOLVING expressions (where possible). > > > >Dick Pierce > > > > Why NOT use MACSYMA? It already exists, and it does everything you want. > Why not try it? There's a very readable tutorial on MACSYMA in the March 1985 issue of the Journal of Symbolic Computation (vol 1 number 1), by Pavelle and Wang. Peter Ladkin