machine learning - Can you "teach" computers to do algebra using variable expressions (eg aX+bX=(a+b)X) -

machine learning - Can you "teach" computers to do algebra using variable expressions (eg aX+bX=(a+b)X) -

let's in illustration lower case constant , upper case variable.

i'd have programs can "intelligently" specified tasks algebra, teaching programme new methods should easy using symbols understood humans. illustration if programme told these facts:

ax+bx=(a+b)x

if a=bx x=a/b

then should able perform these operations: 2a+3a=5a

3x+3x=6x

3x=1 hence x=1/3

4x+2x=1 -> 6x=1 hence x= 1/6

i trying similar things prolog can "understand" variables, had many complications, because 2 describing relationship both ways results in crash. (not easy sort out)

to summarise: want know if programme can taught algebra using mathematic symbols only. i'd know if other people have tried , how complicated expected be. purpose of create programming easier (runtime not important)

it depends on want machine , how intelligent should be.

your question ai not ml. ai deals formalization of "human" tasks while ml (though beingness subset of ai) building models data.

described programme may implemented this:

each fact form pattern. programme given look , patterns can seek apply of them look , see happens. if want programme able to, example, solve quadratic equations given rule ax² + bx + c = 0 → x = (-b ± sqrt(b²-4ac))/(2a) it'd designed follows:

somebody gives set of rules. rule consists of pattern , outcome (solution or equivalent form). think pattern kind of regular expression.

then programme asked show intelligence , prove knowledge via doing given expression. here comes major part:

you build graph of expressions applying possible rules (if pattern applicable look add together new vertex corresponding outcome). then run path-search algorithm (a*, example) find sequence of transformations leading form x = ...

machine-learning artificial-intelligence