Class Polynom

ASCIIMath rendering of the current state (terminal output, not chainable).

Factors of the polynom, computed by factorize on first access and kept until the polynom changes. The zero polynom has none.

Number of monoms.

A detached copy of the monoms (each one cloned). Mutating the returned array or its monoms does NOT affect the polynom — go through add / subtract / multiply / the monoms setter to modify it.

Number of distinct variables.

Expression to give to a plotting tool: explicit * between a coefficient and its variables.

Roots of the polynom, as Solutions sorted by value. A constant polynom has none. The result is kept until the polynom changes.

LaTeX rendering of the current state (terminal output, not chainable).

Numeric value of a constant polynom, or undefined when the degree is not zero.

The variables of the polynom, sorted alphabetically.

Add polynoms, monoms, numbers or strings, then reduce. Modifies and returns the receiver. A string is read as a polynom ("2x+1"). Every operand is built before the receiver is touched: an invalid value throws and leaves it unchanged.

Full duplicate of this instance, including display state (selected form and options set via as*** / with***). Distinct from copy.

Greatest monom dividing every term: gcd of the numerators over gcd of the denominators, and the lowest exponent of each variable (2x^3+6x^2 gives 2x^2).

Copy the mathematical state (monoms and default variable) of another polynom into this one. Display state is not transferred — see clone.

Degree of the polynom as a fraction. Without variable, the highest total degree of a term; with one, the highest exponent of that variable.

Derivative with respect to variable (default x), as a new reduced polynom.

Divide in place. Polynom division is only defined when it is exact.

Remove every monom. Unlike zero, which holds the monom 0, the polynom then has no term at all.

Euclidean division of this polynom by P.

Value of the polynom for given values of its variables.

Value of the polynom for given values of its variables.

Value of the polynom for given values of its variables.

Factorize a polynom with respect to a single variable and store the best results in factors. The variable is the explicit variable, else the sole variable of a single-variable polynom, else the default variable. Multi-variable factorization (treating other variables as symbolic constants) is not supported — the numeric solver cannot represent roots that depend on other variables.

Greatest common divisor of the denominators of the coefficients.

Greatest common divisor of the numerators of the coefficients.

Coefficients from the highest degree down to the constant term (zeros included). Assumes a single variable.

Denominator of the coefficient of each monom, in the order of the monoms.

Numerator of the coefficient of each monom, in the order of the monoms.

Whether the polynom contains a cross-term monom (a single monom carrying more than one variable, such as xy).

True when the variable appears in a term with a non-zero exponent.

Definite integral between a and b, as a fraction. The variable is resolved like in limitTo: the one passed, else the only variable of the polynom, else the default variable.

1/P is not a polynom: the operation is not available.

Whether the given string is the fully developed (expanded) form of this polynom.

True when the division by div leaves no remainder. A degree-1 divisor is tested through its root.

True when both polynoms are equal once reduced and sorted: same terms, same coefficients.

True for the constant polynom 1.

True when P is the opposite polynom (x+1 and -x-1).

True when both polynoms have the same terms, whatever their coefficients (x^2+x and 3x^2-5x).

True for the zero polynom (no term, or the single term 0).

Least common multiple of the denominators of the coefficients.

Least common multiple of the numerators of the coefficients.

Limit of the polynom as its variable approaches value. An infinite value returns a signed infinite Fraction, determined by the leading term (and the degree parity at -∞).

Monom of the given degree for variable, or the monom of highest degree when degree is omitted. Returns the zero monom when none matches.

First monom that contains variable, or the zero monom when none does.

Every monom of the given degree for variable, or of the highest degree when degree is omitted.

Multiply by polynoms, monoms, fractions, numbers or strings, then reduce. Modifies and returns the receiver. A string is read as a polynom ("x+3"). Every operand is built before the receiver is touched: an invalid value throws and leaves it unchanged.

Set the polynom to the constant 1.

Change the sign of every term.

Route an input to the matching from*** builder. This method only dispatches on the input's type/format; it never inlines construction.

Raise to a non-negative integer power; the power 0 gives 1.

A primitive with respect to variable (default x), without integration constant.

Add the similar terms, remove the zero terms, reduce the coefficients and sort by decreasing degree.

Sort the monoms by decreasing degree of variable (default: the default variable of the polynom), or by increasing degree when revert is true. The other variables break the ties.

Replace a variable by a polynom (in place).

The n-th root of a polynom is not a polynom: the operation is not available.

Set the default variable, used when a method needs one and the polynom does not decide it.

The square root of a polynom is not a polynom: the operation is not available.

Subtract polynoms, monoms, numbers or strings, then reduce. Modifies and returns the receiver. A string is read as a polynom ("x-1"). Every operand is built before the receiver is touched: an invalid value throws and leaves it unchanged.

Set the polynom to zero.

Build a polynom from coefficients ordered highest→lowest degree. The first argument is the variable (e.g. 'x', 't').

Build a constant polynom.

Build a multivariate linear polynom: 'xyz', a, b, c, d → ax + by + cz + d.

Build a polynom from monoms, or from anything a monom accepts (numbers, strings, fractions). The result is neither reduced nor sorted: call reduce.

Build a polynom from an expression: sums, products, integer powers, and division by a constant.

Build the polynom of degree at most 2 passing through three points, using Newton divided differences. The result is exact (fractions). When the three points are aligned, the result is a line (degree 1), or a constant when the three y are equal.

Product of the given values, as a new polynom.