How do I pass in a polynomial function in java?

Question

For a programming project in Calculus we were instructed to code a program that models the Simpson's 1/3 and 3/8 rule.

We are supposed to take in a polynomial(i.e. 5x^2+7x+10) but I am struggling conceptualizing this. I have began by using scanner but is there a better way to correctly read the polynomial?

Any examples or reference materials will be greatly appreciated.

how about in a list where the index tells you which degree the number is? (example list[10,7,5]) — gtgaxiola, Mar 04 '13 at 18:40
Or are you asking how to parse user input to get the polynomial? — Reinstate Monica -- notmaynard, Mar 04 '13 at 18:42
I believe parsing is my problem. I am somewhat new to java so this is troubling me. — user2132947, Mar 04 '13 at 18:44
@gtgaxiola that's a great idea. `list[i]` gives the coefficient of `x^i`. — Andrew Mao, Mar 04 '13 at 18:44
@user2132947 How are you getting your input? (from Arguments, raw input, a file, your choice, etc) — gtgaxiola, Mar 04 '13 at 18:46
So when the user enters a polynomial store the exponents in an array? — user2132947, Mar 04 '13 at 18:47
This might help you: http://stackoverflow.com/questions/4130523/validating-polynomials-from-a-string/4130888#4130888 — Reinstate Monica -- notmaynard, Mar 04 '13 at 18:48
@gtgaxiola Im reading in input from scanner, or at least trying to. — user2132947, Mar 04 '13 at 18:48
After you get your input args into your program, use a Map to store your values. The first Integer could be your exponent, and the second could be your value. The requirements for Map prevent duplicate items, so you would have unique values for each exponent. — bakoyaro, Mar 04 '13 at 19:08
On another note, welcome to stackoverflow! It looks like you could use some rep... +1 for you! — bakoyaro, Mar 04 '13 at 19:10
@bakoyaro Thank you very much! I am totally new to this type of website and I appreciate all the input from above. I will look up the Map technique you suggested. Thank you once more! — user2132947, Mar 04 '13 at 19:12

score 1 · Answer 1 · answered Mar 04 '13 at 18:47

1

A simple way (to get you started) is to use an array.
In your example: 5x^2 + 7x + 10 would be:
{10,7,5}
I.e. at index 0 is the factor 10 for x^0 at index 1 is 7 for x^1 at index 2 is 10 for x^2.

Of course this not the best approach. To figure out way figure out how you would represent x^20

answered Mar 04 '13 at 18:47

Cratylus

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Thank You very much Cratylus I will give that approach a shot! thank you as well @Sotirios Delimanolis – user2132947 Mar 04 '13 at 18:55

Bill K · Answer 2 · 2013-03-04T18:54:32.673

In java it would be easiest to pre-format your input and just ask for constants--as in, "Please enter the X^2 term" (and then the X term, and then the constant).

If that's not acceptable, you are going to be quite vulnerable to input style differences. You can separate the terms by String.split[ting] on + and -, that will leave you something like:

[5x^2], [7x], [10]

You could then search for strings containing "x^2" and "x" to differentiate your terms

Remove spaces and .toLowerCase() first to counter user variances, of course.

When you split your string you will need to identify the - cases so you can negate those constants.

You could do two splits, one on + the other on -. You could also use StringTokenizer with the option to keep the "Tokens" which might be more straight-forward but StringTokenizer makes some people a little uncomfortable, so go with whatever works for you.

Note that this will succeed even if the user types "5x^2 + 10 + 7 x", which can be handy.

What if the type of polynomial is not limited exponentially? So the input could be a function (4x^7 + 10x^4 +3x + 10) or ( x^3)? — user2132947, Mar 04 '13 at 19:00
You have to make some assumptions about the input or build a general calculator. The more assumptions you make, the easier it is. Your suggested input wouldn't cause any difficulty, just a slight modification to pull off the powers as well as the constants... — Bill K, Mar 04 '13 at 21:23

duffymo · Accepted Answer · 2013-03-04T19:31:33.670

1

I'd suggest that you start with a Function interface that takes in a number of input values and returns an output value:

public interface Function {
    double evaluate(double x);
}

Write a polynomial implementation:

public class Poly {

    public static double evaluate(double x, double [] coeffs) {
        double value = 0.0;
        if (coeffs != null) {
            // Use Horner's method to evaluate.
            for (int i = coeffs.length-1; i >= 0; --i) {
                value = coeffs[i] + (x*value);
            }
        }
        return value;
    }
}

Pass that to your integrator and let it do its thing.

edited Mar 04 '13 at 19:31

answered Mar 04 '13 at 18:54

duffymo

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In your example, instead of hardcoding values(10.0, 7.0, 5.0) I could very well pass the coefficients that are consistent with the function the user entered in, correct? – user2132947 Mar 04 '13 at 19:05

score 0 · Answer 4 · edited Jun 20 '20 at 09:12

I believe parsing is my problem. I am somewhat new to java so this is troubling me.

You should use a parser generator.

A parser generator is a tool that reads a grammar specification and converts it to a Java program that can recognize matches to the grammar. In addition to the parser generator itself, JavaCC provides other standard capabilities related to parser generation such as tree building (via a tool called JJTree included with JavaCC), actions, debugging, etc.

JavaCC's FAQ answers How do I parse arithmetic expressions?

See the examples that come with JavaCC.

See any text on compiling.

See Parsing Epressions by Recursive Descent and a tutorial by Theodore Norvell.

Also, see JavaCC - Parse math expressions into a class structure

How do I pass in a polynomial function in java?

4 Answers4