When we attended middle school were asked to simplify mathematical expressions like "3x-yx+2xy-x" (or usually bigger), and that was easy-peasy ("2x+xy"). But tell that to your pc and we'll see!
Write a function: simplify, that takes a string in input, representing a multilinear non-constant polynomial in integers coefficients (like "3x-zx+2xy-x"), and returns another string as output where the same expression has been simplified in the following way ( -> means application of simplify):
- All possible sums and subtraction of equivalent monomials ("xy==yx") has been done, e.g.:
"cb+cba" -> "bc+abc","2xy-yx" -> "xy","-a+5ab+3a-c-2a" -> "-c+5ab" - All monomials appears in order of increasing number of variables, e.g.:
"-abc+3a+2ac" -> "3a+2ac-abc","xyz-xz" -> "-xz+xyz"
- If two monomials have the same number of variables, they appears in lexicographic order, e.g.:
"a+ca-ab" -> "a-ab+ac","xzy+zby" ->"byz+xyz"
- There is no leading
+sign if the first coefficient is positive, e.g.:
"-y+x" -> "x-y", but no restrictions for-:"y-x" ->"-x+y"
N.B. to keep it simplest, the string in input is restricted to represent only multilinear non-constant polynomials, so you won't find something like `-3+yx^2'. Multilinear means in this context: of degree 1 on each variable.
Warning: the string in input can contain arbitrary variables represented by lowercase characters in the english alphabet.
Good Work :)