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math/calculus - symbolic integration and differentiation

The math/calculus addon serves as a library replacement for the d. and D. primitives supplied in older versions of J.

The hope here is that, by implementing these mechanisms with library code, they might be more easily extended to handle cases previously not handled.

Example use:

   *: deriv_jcalculus_ 1(i. 10)
0 2 4 6 8 10 12 14 16 18

Here, the left argument to one of these conjunctions is a verb whose monadic definition would be integrated or differentiated. and the right argument indicates how to proceed (1 means differentiate once, 2 means differentiate twice, etc. negative numbers specify integration, the constant of integration used here is 0 -- other constants of integration can be added "manually".)

  • deriv_jcalculus_ replaces d.
  • pderiv_jcalculus_ replaces D.
  • derivsecant_jcalculus_ replaces D: where the x and y arguments to the derived function determine the points to be used (y and y+x) in calculating the secant slope.