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I'm writing a software that does simple mathematical calculations for lazy people.

I need ideas. I already wrote some pieces of code that calculates 'Quadratic formula', but I have no idea what to do next.

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Stop coding and spread links to – Raphael Jan 4 '11 at 16:00
You could better contribute to Maxima or Sage once you're good enough. Solving quadratic equations in software is very trivial. Try doing symboling integration. – Jonas Teuwen Jan 4 '11 at 16:17
You might find this interesting: It is not quite what you were asking for, but it contains many math problems that one must use programming to solve. – Vitaly Lorman Jan 4 '11 at 16:19
I've seen so many little apps that solve quadratics, and they're good programming exercises, but imho they shouldn't be released because they're just a lot of dressed up code for solving a trivial problem. If you want to do something more challenging and useful: 1) Try coding something that numerically solves a univariate polynomial of n'th order; 2) Extend that to solve multivariate polynomial systems of n'th order (numerically); 3) Learn the theory behind Groebner bases, and symbolically solve multivariate polynomial systems of n'th order. – Gilead Jan 4 '11 at 16:24
To the commenters: do click on the OP's page and check out his profile. I agree completely with the content of the replies, but I think it's an investment in the future not to be too discouraging to young people. – Pete L. Clark Jan 4 '11 at 20:15

I'm with Jonas T, I don't know why he didn't make his comment an answer.

Symbolic integration of polynomials would be an easy next step.

I disagree somewhat with Raphael. Coding some simple functions can give you a better appreciation when you do use something like WolframAlpha.

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