sicmutils.calculus.derivative — sicmutils 0.14.0

canonicalize-differential clj/s

(canonicalize-differential dx)

D clj/s

Derivative operator. Produces a function whose value at some point can multiply an increment in the arguments, to produce the best linear estimate of the increment in the function value.

derivative clj/s

(derivative f)

derivative-symbol clj/s

Differential cljs

differential-of clj/s

(differential-of dx)

The differential of a quantity is, if we're a differential, the differential of the coefficient of the highest-order term part, or else the input itself.

differential? clj/s

(differential? x)

dx*dy clj/s

(dx*dy dx dy)

Form the product of the differentials dx and dy.

dx+dy clj/s

(dx+dy dx dy)

Adds two objects differentially. (One of the objects might not be differential; in which case we lift it into a trivial differential before the addition.)

make-differential clj/s

(make-differential tags->coefs)

The input here is a mapping (loosely defined) between sets of differential tags and coefficients. The mapping can be an actual map, or just a sequence of pairs. The differential tag sets are sequences of integer tags, which should be sorted.

max-order-tag clj/s

(max-order-tag ds)

From each of the differentials in the sequence ds, find the highest order term; then return the greatest tag found in any of these terms; i.e., the highest-numbered tag of the highest-order term.

partial clj/s

(partial & selectors)

Partial differentiation of a function at the (zero-based) slot index provided.

taylor-series clj/s

(taylor-series f x dx)

Returns a Series of the coefficients of the taylor series of the function f evaluated at x, with incremental quantity dx.

NOTE: The (constantly dx) term is what allows this to work with arbitrary structures of x and dx. Without this wrapper, ((g/* dx D) f) with dx == (up 'dx 'dy) would expand to this:

(fn [x] (* (s/up ('dx x) ('dy x)) ((D f) x)))

constantly delays the interpretation of dx one step:

(fn [x] (* (s/up 'dx 'dy) ((D f) x)))

with-and-without-tag clj/s

(with-and-without-tag tag dx)

Split the differential into the parts with and without tag and return the pair

with-tag clj/s

(with-tag tag dx)

The differential containing only those terms with the given tag

without-tag clj/s

(without-tag tag dx)

The differential containing only those terms without the given tag