sicmutils.polynomial — io.samritchie/sicmutils 0.13.0-SNAPSHOT

abs clj/s

(abs p)

add clj/s

(add p q)

Adds the polynomials p and q

check-same-arity clj/s

(check-same-arity p q)

coefficient clj/s

coefficients clj/s

(coefficients p)

degree clj/s

(degree p)

divide clj/s

(divide u v)

Divide polynomial u by v, and return the pair of [quotient, remainder] polynomials. This assumes that the coefficients are drawn from a field, and so support division.

evaluate clj/s

(evaluate p xs)

Evaluates a multivariate polynomial p at xs.

evenly-divide clj/s

(evenly-divide u v)

Divides the polynomial u by the polynomial v. Throws an IllegalStateException if the division leaves a remainder. Otherwise returns the quotient.

exponents clj/s

expt clj/s

(expt p n)

Raise the polynomial p to the (integer) power n.

graded-lex-order clj/s

(graded-lex-order xs ys)

graded-reverse-lex-order clj/s

(graded-reverse-lex-order xs ys)

lex-order clj/s

(lex-order xs ys)

Lex order for monomials considers the power of x, then the power of y, etc.

lower-arity clj/s

(lower-arity p)

Given a nonzero polynomial of arity A > 1, return an equivalent polynomial of arity 1 whose coefficients are polynomials of arity A-1.

make clj/s

(make dense-coefficients)

(make arity xc-pairs)

When called with two arguments, the first is the arity (number of indeterminates) of the polynomial followed by a sequence of exponent-coefficient pairs. Each exponent should be a vector with length equal to the arity, with integer exponent values. To make 4 x^2 y + 5 x y^2, an arity 2 polynomial (since it has two variables, x and y), we could write the following for xc-pairs: [[[2 1] 4] [[1 2] 5]]

When called with one argument, the sequence is interpreted as a dense sequence of coefficients of an arity-1 (univariate) polynomial. The coefficients begin with the constant term and proceed to each higher power of the indeterminate. For example, x^2

• 1 can be constructed by (make [-1 0 1]).

make-constant clj/s

(make-constant arity c)

Return a constant polynomial of the given arity.

map-coefficients clj/s

(map-coefficients f p)

Map the function f over the coefficients of p, returning a new Polynomial.

map-exponents clj/s

(map-exponents f p)

Map the function f over the exponents of each monomial in p, returning a new Polynomial.

monomial? clj/s

(monomial? p)

mul clj/s

(mul p q)

Multiply polynomials p and q, and return the product.

negate clj/s

partial-derivative clj/s

(partial-derivative p i)

The partial derivative of the polynomial with respect to the i-th indeterminate.

partial-derivatives clj/s

(partial-derivatives p)

The sequence of partial derivatives of p with respect to each indeterminate

polynomial? clj/s

(polynomial? p)

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

pseudo-remainder clj/s

(pseudo-remainder u v)

Compute the pseudo-remainder of univariate polynomials p and q. Fractions won't appear in the result; instead the divisor is multiplied by the leading coefficient of the dividend before quotient terms are generated so that division will not result in fractions. Only the remainder is returned, together with the integerizing factor needed to make this happen. Similar in spirit to Knuth's algorithm 4.6.1R, except we don't multiply the remainder through during gaps in the remainder. Since you don't know up front how many times the integerizing multiplication will be done, we also return the number d for which d * u = q * v + r.

raise-arity clj/s

(raise-arity p)

The opposite of lower-arity.

sub clj/s

(sub p q)

Subtract the polynomial q from the polynomial p.