Need some help about computer programming.

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In mathematics, sometimes we have to do very long and time consuming work related to some functions or algorithm or some other work. For example if we want to check that for which last number $n$, $0$ Comes in the expansion of $3^n$ For another example, take partition function. If we want to find some relation we have to apply that practically on numbers. It takes very much time and energy. I have heard that we can setup a programme in computer to do this work. Can anyone help me about this? I am in 9th grade.

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If you consider spending money, I would suggest Wolfram's Mathematica. It can do pretty much everything related to maths in just a few lines of input. Almost no programming skills required.

Otherwise, using Python or Java is possible too, but you have to learn the language first and write more code for the same results. Yet I'm sure it won't take you too long, since using either on a "mathematical" level is pretty much straightforward.

You just have to download an developing environment and you're ready to go. Additionally, you can find lots of code samples for mathematical functions on the internet.

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You could easily do that. In order to do that you have to first learn a programming language. I recommend Python for starting. It's an easy language which is widely used among scientists.