Resources
At the time of this revision, there is very little known documentation on how to program Nspire calculators. Below is a list of resources that contain information on Nspire Basic.
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This article details how to make a program on Nspire family calculators.
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TI Codes by Texas Instruments contains some basic information on how to program an Nspire.
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The TI-Nspire Programming eGuide, made by TI, should have documentation of most Nspire commands.
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This page provides some basic information on how to do Lua Scripting on an Nspire.
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This YouTube playlist has several videos showing how to do algebraic things on Nspire calculators.
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This page by TI-Basic Wikia shows some of the basics of Nspire programming.
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This wiki contains some information on a variety of Nspire topics, including how to hack an Nspire.
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This site details Lua scripting for Nspire calculators. (As a side note, the more research I do, the more it seems that Lua scripting is the easiest way to make advanced Nspire programs...)
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This is a guide to programming an Nspire CX, but it isn't free.
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This Cemetech discussion has information on doing Micro Python programming on an Nspire.
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This article by TI-Planet details how to program Nspires in Micro Python.
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This Nspire manual over at manualslib has some information on programming.