A while back I wanted to upgrade my Polynomials All-In-One program which added, subtracted, multiplied, and divided polynomials. It also could do derivative, integral, and zeroes. I hoped to allow it to auto-order of operations parse. I still could not implement an efficient order of operations parser, so I settled for the next best.
You type a list of operators, followed by a colon, followed by a bracket-enclosed list of polynomials (I could change the brackets to parenthases if people prefer it). For example, to do:
(3x^2 - 7x +2) - (4x - 4) * (x^2 + 4x - 1)
you would type at the prompt:
-*:{3x^2-7x+2}{4x-4}{x^2+4x-1}
Additionally, the letters D, I, and Z (and their lowercase counterparts) will add derivative, integral, and zeroes to the computation queue. Zeroes simply displays the zeroes, but doesn't affect the prior value, allowing the queue to resume after doing zeroes as normal.
Here's two screenshots of the program doing a few simple operations. Anyone who wants to beta test it can download it here.
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BUGS I KNOW OF: Dividing with a 1-term denominator gives a Domain error on the deltaList line; Doing a derivative or integral as the first and only argument gives a domain error due to the string->list conversion (now resolved but not in the beta uploaded)
Also, the program currently discards any remainders from division. If someone can advise me on how to use it, I'll try to.