Core to working with algebra problems is the ability to
combine like terms in polynomials, and Mathy provides an environment that generates problems that require simplification to satisfy the win-conditions.
In Poly Simplify the agent must learn to quickly combine and simplify all the like terms in the generated input expression.
4x + 2y + 2xmust be simplified to
6x + 2y
23j + 7 + 12x + 2jmust be simplified to
25j + 7 + 12x
1.3j + 2j - 7must be simplified to
3.3j - 7
A problem is considered solved when there are no remaining like terms in the expression, and all terms are expressed in a simple way.
No Like Terms¶
Terms are like when they share a common variable and exponent and are connected by an addition or subtraction.
4x + 2ythere are no like terms because
yare different variables
2x^2 + 4xthere are no like terms because
xhave different exponents
82x + 14xthe terms are like because
xare the same
12x + 12ythere are no like terms because
No Complex Terms¶
Terms are considered complex when there's a more concise way they could be expressed.
2 * 4xis complex because it has multiple coefficients which could be simplified to
4x * y * j^2is not complex despite being verbose because there is only a single coefficient and no matching variables
A trained agent learns to combine multiple low-level actions into higher-level ones that
combine like terms
1k + 210r + 7z + 11k + 10z
|input||1k + 210r + 7z + 11k + 10z|
|commutative swap||11k + (1k + 210r + 7z) + 10z|
|distributive factoring||11k + (1k + 210r) + (7 + 10) * z|
|distributive factoring||(11 + 1) * k + 210r + (7 + 10) * z|
|constant arithmetic||(11 + 1) * k + 210r + 17z|
|constant arithmetic||12k + 210r + 17z|
|solution||12k + 210r + 17z|
12k + 210r + 17z