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sicmutils.calculus.derivative


canonicalize-differentialclj/s

(canonicalize-differential dx)

Dclj/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 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.
raw docstring

derivativeclj/s

(derivative f)

differential-ofclj/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.

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.
raw docstring

differential?clj/s

(differential? x)

dx*dyclj/s

(dx*dy dx dy)

Form the product of the differentials dx and dy.

Form the product of the differentials dx and dy.
raw docstring

dx+dyclj/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.)

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.)
raw docstring

make-differentialclj/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.

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.
raw docstring

max-order-tagclj/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.

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.
raw docstring

partialclj/s

(partial & selectors)

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

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

taylor-series-termsclj/s

(taylor-series-terms f x dx)

The (infinite) sequence of terms of the taylor series of the function f evaluated at x, with incremental quantity dx.

The (infinite) sequence of terms of the taylor series of the function f
evaluated at x, with incremental quantity dx.
raw docstring

with-and-without-tagclj/s

(with-and-without-tag tag dx)

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

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

with-tagclj/s

(with-tag tag dx)

The differential containing only those terms with the given tag

The differential containing only those terms with the given tag
raw docstring

without-tagclj/s

(without-tag tag dx)

The differential containing only those terms without the given tag

The differential containing only those terms without the given tag
raw docstring

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