sicmutils.rational-function — sicmutils 0.21.1

->expression clj/s

(->expression r vars)

Accepts a RationalFunction r and a sequence of symbols for each indeterminate, and emits the canonical form of the symbolic expression that represents RationalFunction r.

NOTE: this is the output stage of Rational Function canonical form simplification. The input stage is handled by expression->.

NOTE See analyzer for an instance usable by sicmutils.expression.analyze/make-analyzer.

abs clj/s

(abs r)

If the numerator of r is negative, returns (negate r), else acts as identity.

add clj/s

(add r s)

Returns the sum of rational functions r and s, with appropriate handling of RationalFunction, polynomial/Polynomial or coefficients of neither type on either side.

analyzer clj/s

Singleton [[a/ICanonicalize]] instance.

arg-scale clj/s

(arg-scale r factors)

Given some RationalFunction r, returns a new RationalFunction generated by substituting each indeterminate x_i for f_i * x_i, where f_i is a factor supplied in the factors sequence.

Given a non-RationalFunction, delegates to polynomial/arg-scale.

arg-shift clj/s

(arg-shift r shifts)

Given some RationalFunction r, returns a new RationalFunction generated by substituting each indeterminate x_i for s_i + x_i, where s_i is a shift supplied in the shifts sequence.

Given a non-RationalFunction, delegates to polynomial/arg-shift.

arity clj/s

(arity r)

Returns the declared arity of the supplied RationalFunction or polynomial/Polynomial, or 0 for arguments of other types.

coeff? clj/s

(coeff? x)

Returns true if x is explicitly not an instance of RationalFunction or polynomial/Polynomial, false if it is.

cube clj/s

(cube r)

Returns the cube of rational function r. Equivalent to (mul r (mul r r)).

div clj/s

(div r s)

Returns the quotient of rational functions r and s, with appropriate handling of RationalFunction, polynomial/Polynomial or coefficients of neither type on either side.

eq clj/s

(eq this that)

Returns true if the RationalFunction this is equal to that. If that is a RationalFunction, this and that are equal if they have equal u and v and equal arity. u and v entries are compared using sicmutils.value/=.

If that is non-RationalFunction, eq only returns true if u and v respectively match the [[ratio/numerator]] and [[ratio/denominator]] of that.

evaluate clj/s

(evaluate r xs)

Given some rational function xs and a sequence of arguments with length >= 0 and < the arity of r, returns the result of evaluating the numerator and denominator using xs and re-forming a rational function with the results.

Supplying fewer arguments than the arity will result in a partial evaluation. Supplying too many arguments will error.

expression-> clj/s

(expression-> expr)

(expression-> expr cont)

(expression-> expr cont v-compare)

Converts the supplied symbolic expression expr into Rational Function canonical form (ie, a RationalFunction instance). expr should be a bare, unwrapped expression built out of Clojure data structures.

Returns the result of calling continuation cont with the RationalFunction and the list of variables corresponding to each indeterminate in the RationalFunction. (contdefaults to vector).

The second optional argument v-compare allows you to provide a Comparator between variables. Sorting indeterminates by v-compare will determine the order of the indeterminates in the generated RationalFunction. The list of variables passed to cont will be sorted using v-compare.

Absorbing an expression with expression-> and emitting it again with ->expression will generate the canonical form of an expression, with respect to the operations in the [[operators-known]] set.

This kind of simplification proceeds purely symbolically over the known Rational Function operations; other operations outside the arithmetic available should be factored out by an expression analyzer (see sicmutils.expression.analyze/make-analyzer) before calling expression->.

NOTE that cont might receive a scalar, fraction or polynomial/Polynomial instance; both are valid 'rational functions'. The latter as a rational function with a denominator equal to 1, and the former 2 result from non-polynomial numerator and denominator.

NOTE See analyzer for an instance usable by sicmutils.expression.analyze/make-analyzer.

expt clj/s

(expt r n)

Returns a rational function generated by raising the input rational function r to the (integer) power n.

from-points clj/s

(from-points xs)

Given a sequence of points of the form [x, f(x)], returns a rational function that passes through each input point.

gcd clj/s

(gcd r s)

Returns the greatest common divisor of rational functions r and s, with appropriate handling of RationalFunction, polynomial/Polynomial or coefficients of neither type on either side.

invert clj/s

(invert r)

Given some rational function r, returns the inverse of r, ie, a rational function with numerator and denominator reversed. The returned rational function guarantees a positive denominator.

Acts as generic/invert for non-RationalFunction inputs.

make clj/s

(make u v)

Given a numerator u and denominator v, attempts to form a RationalFunction instance by

• cancelling out any common factors between u and v
• normalizing u and v such that v is always positive
• multiplying u and v through by a commo factor, such that neither term contains any rational coefficients

Returns a RationalFunction instance if either u or v remains a polynomial/Polynomial after this process; else, returns (g/div u' v'), where u' and v' are the reduced numerator and denominator.

mul clj/s

(mul r s)

Returns the product of rational functions r and s, with appropriate handling of RationalFunction, polynomial/Polynomial or coefficients of neither type on either side.

negate clj/s

(negate r)

Returns the negation of rational function r, ie, a RationalFunction with its numerator negated.

Acts as generic/negate for non-RationalFunction inputs.

negative? clj/s

(negative? r)

Returns true if the numerator of r is polynomial/negative?, false otherwise.

partial-derivative clj/s

(partial-derivative r i)

Given some RationalFunction or polynomial/Polynomial r, returns the partial derivative of r with respect to the ith indeterminate. Throws if i is an invalid indeterminate index for r.

For non-polynomial or rational function inputs, returns 0.

partial-derivatives clj/s

(partial-derivatives r)

Returns the sequence of partial derivatives of RationalFunction (or polynomial/Polynomial) r with respect to each indeterminate. The returned sequence has length equal to the arity of r.

For non-polynomial or rational function inputs, returns an empty sequence.

rational-function? clj/s

(rational-function? r)

Returns true if the supplied argument is an instance of RationalFunction, false otherwise.

RationalFunction cljs

square clj/s

(square r)

Returns the square of rational function r. Equivalent to (mul r r).

sub clj/s

(sub r s)

Returns the difference of rational functions r and s, with appropriate handling of RationalFunction, polynomial/Polynomial or coefficients of neither type on either side.