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A struggling manufacturer named Tennessee Instrumental is desperate to get into the calculator business. Problem is, they don't have any software engineers on payroll, and the deadline is coming up fast.
It's your job to help TI configure a basic calculus-ready calculator that can simplify expressions input as strings, and as a bonus (since they're on such a tight schedule), they don't care what language you use to get there! They do, however, care about how much space you take up. Not very good with hardware, it seems. Keep it brief, fewest bytes gets you hired.
Goal
Create a function which can simplify a basic calculus expression
Your calculator must be able to perform the following operations:
+Addition-Subtraction and Negation*Multiplication/Division^Exponentiation()Parenthetical Reduction()'Derivation (first order)
Your calculator must also be able to use x as a placeholder variable. Do not solve for x. That will come in time.
Input
Input is a string containing the plaintext version of the expression you're looking to simplify. The only valid input characters are 0-9, x, +, -, *, /, ^, (), ', and . Some examples of valid inputs are listed below:
"1"
"5 + 8"
"(5x + 3)(4x + 2)"
"4x - 9x + 15"
"24x / 6"
"5x^2 + 14x - 3" // Use ^ for exponentiation
"(20x^2)'" // Use ()' for derivation
Output
Output is a string containing the plaintext version of the expression after simplification.
The only acceptable operators left over are +, -, /, and ^. Multiples of variables should be indicated as 2x, -5x, etc. Fractions should be reduced as far as possible, and parentheses and derivations must be completely eliminated, with the exception of cases such as ln(x) which syntactically cannot be made to make sense without them.
The input examples from above should output as follows:
"1" => "1"
"5 + 8" => "13"
"(5x + 3)(4x + 2)" => "20x^2 + 22x + 6"
"4x - 9x + 15" => "-5x + 15"
"24x / 6" => "4x"
"5x^2 + 14x - 3" => "5x^2 + 14x - 3"
"(20x^2)'" => "40x"
Last but not least, if a derivation function exists in your language, you may not use it. Derivations must be done as manually as possible. Whitespace around the basic four operators and lack of whitespace around ^ and within () is preferred.
ricdesi
Posted 2016-02-25T15:19:18.727
Reputation: 499
What about if my language has a built-in symbolic calculator? Also,
1x/2or1/2xor0.5xorx/2? – Lynn – 2016-02-25T15:30:33.910When you say we're not allowed to use a built-in symbolic differentiator, are we allowed to use built-in functions for everything else? – A Simmons – 2016-02-25T15:31:53.213
@ASimmons I'd say the rest is probably acceptable - what did you have in mind? – ricdesi – 2016-02-25T15:33:36.510
@Lynn
x/2is the preferred answer,1/2xis a different value altogether (1/(2x)reduced). – ricdesi – 2016-02-25T15:35:13.713I usually work in Mathematica so converting the string to an expression would yield a reduced version. – A Simmons – 2016-02-25T15:37:34.820
@ASimmons Ah, I see what you mean. I'll allow it, it's definitely a big advantage but them's the breaks. – ricdesi – 2016-02-25T15:40:44.460
Very related – Robert Fraser – 2016-02-25T15:45:45.020
The spec states that "parentheses and derivations must be completely eliminated", but that isn't necessarily possible with the set of operators given. E.g.
(2^x)'requireslnto eliminate the derivative. – Peter Taylor – 2016-02-25T16:10:47.203@PeterTaylor Good catch! I will amend the question – ricdesi – 2016-02-25T16:11:34.437
1For clarification: I voted to close as too broad, despite what the banner says. – Mego – 2016-02-25T21:47:35.050