Derivative of Polynomial with unknown term count?

[lxXTaCoXxl]

I'm trying to upgrade my class library to my current mathematical skill set and am having trouble with multi-term polynomials, especially those I where I don't know how many terms the user will be putting in. I know that the formula for the first derivative of a polynomial is ax^n = n * ax^n-1; and the second derivative is the derivative of the first derivative. So for example:

Find the derivative of 4x^2:
4x^2 = 2 * 4x^2 - 1 = 8x^2-1 = 8x

Find the second derivative of 4x^3:
4x^3 = 3 * 4x^3-1 = 12x^3-1 = 12x^2
12x^2 = 2 * 12x^2-1 = 24x^2-1 = 24x

Right now I just have an algorithm for the first derivative of a single term polynomial:

// Pseudocode (C# Syntax):
public string DerivativeOfPolynomial(int Base, string Variable, int Exponent) {
    Base = Exponent * Base;
    Exponent = Exponent > 1 ? Exponent - 1 : 0;
    Variable = Exponent == 0 ? "" : Variable;

    return Base.ToString() + Variable + (Exponent == 0 ? "" : Exponent).ToString();
}

Chose to not work on the second derivatives until I figure out the whole parameter problem. I'm sure I have to use arrays or lists to accomplish this, but I'm not sure how the algorithm would work for a polynomial with 3 terms:

3x^2 + 13x + 4

Also the derivative of a constant (basically any number without a variable and exponent of 2 or higher) is equal to 0 for those who don't know.

[thines01]

Dot net collections are good for unknown amounts of something (like a list).
You can even make an extension method on the list to process the elements throught he functions.

[lxXTaCoXxl]

For example? LOL

I knew that I should use a list, but the problem is how do I read each one as part of each polynomial:

// Pseudocode:
private string DerivativeOfPolynomial(int[] Bases, string[] Variables, int[] Exponents) {
    string temp = "";
    for (int i = 0; i < Bases.Length; i++) {
        Bases *= Exponents[i] >= 1 ? Exponents[i] : 1;
        Exponents[i] -= Exponents[i] > 1 ? 1 : 0;
        string exTemp = Exponents[i] == 0 ? "" : Exponents[i].ToString();
        Variables[i] = Exponents[i] > 1 ? Variables[i] + "^" : "";

        temp += Bases.ToString() + Variables[i] + exTemp + " :: ";
    }

    return temp;
}

However if all three array lengths are not the same either an exception will be thrown for index out of bounds or not all terms will be simplified.

[skatamatic]

Why not use a class to hold the exponent/variables/bases?

class Term
{
    public int Base {get; set;}
    public string Variable {get; set;}
    public int Exponent {get; set;}
}
private string DerivativeOfPolynomial(IList<Term> terms)
{
    return  string.Join(" ",
        from term in terms
        let tempExponent = term.Exponent - (term.Exponent > 1 ? 1 : 0)
        select ((term.Base * (term.Base >= 1 ? term.Exponent : 1)).ToString() + 
        (tempExponent > 1 ? term.Variable + "^" : "") +
        (tempExponent > 0 ? tempExponent.ToString() : "") + " :: ").ToList());        
}

Edit: I redid your solution with Linq before Thines could lol!

[lxXTaCoXxl]

LOL @skatamatic I was just waiting on your reply, and the people over in the C++ section said to use a struct. But I couldn't "completely" understand the sample they gave because I'm still a little new to C++. However, I like the example you gave, and can at least understand it partially. Could you do me a solid and explain how the 'from' structure you have there is working? I don't completely think I understand the 'let' and select' keywords. From just reading the example it looks like it's creating a new temporary variable called 'tempExponent' then setting the value to the exponent minus the result of a conditional (one or zero). Then as for the select keyword, I have now idea what it is doing. Also, is the structure compatible with C++? Thanks again for the help.

[skatamatic]

I can't remember if C++ supports automatic properties, and it is using a string reference rather than a cstring or character array but it should be pretty transferable to C++ as a class or a struct.

As for the 'from', 'in', 'let' and 'select', you have just seen Linq in action :) I'm not going to explain it much (it's practically a language of its own) but it allows for very syntactically clear and dynamic iteration of collections. The basic idea was to integrate SQL-like queries directly into C# syntax, and allow it to interact with objects. It has grown to support quite a bit and is probably worth your time to look into. Here's a good link. And some examples.

[lxXTaCoXxl]

Thanks, those where very helpful. :)