# Poly Simplify

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.

## Challenge¶

In Poly Simplify the agent must learn to quickly combine and simplify all the like terms in the generated input expression.

Examples

`4x + 2y + 2x`

must be simplified to`6x + 2y`

`23j + 7 + 12x + 2j`

must be simplified to`25j + 7 + 12x`

`1.3j + 2j - 7`

must be simplified to`3.3j - 7`

## Win Conditions¶

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.

Examples

`4x + 2y`

there are no like terms because`x`

and`y`

are**different variables**`2x^2 + 4x`

there are no like terms because`x^2`

and`x`

have**different exponents**`82x + 14x`

the terms are like because`x`

and`x`

are the same`12x + 12y`

there are no like terms because`x`

and`y`

**different variables**

### No Complex Terms¶

Terms are considered complex when there's a more concise way they could be expressed.

Examples

`2 * 4x`

is**complex**because it has**multiple coefficients**which could be simplified to`8x`

`4x * y * j^2`

is**not complex**despite being verbose because there is only a**single coefficient**and**no matching variables**

## Example Episode¶

A trained agent learns to combine multiple low-level actions into higher-level ones that `combine like terms`

### Input¶

`1k + 210r + 7z + 11k + 10z`

### Steps¶

Step | Text |
---|---|

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 |

### Solution¶

`12k + 210r + 17z`