Class Equation

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

Left member. This is the polynom itself, not a copy: use split for copies.

Number of distinct variables in both members.

Right member. This is the polynom itself, not a copy: use split for copies.

Sign of the equation: =, <, >, <= or >=. Setting it accepts the other notations (\leq, geq, =>...).

The sign written for LaTeX: \leq and \geq for the non-strict inequalities.

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

The variables of both members, without duplicates.

Add one or more values to the equation. An Equation operand is added member by member; any other value (Polynom, Monom, Fraction, number, or a sign-less string) is added to both members. Atomic: a failing operand leaves the receiver intact.

Whether the equation can be linearly isolated for the given variable: it must be of the first degree and free of any cross-term monom. Pure query (no mutation); use it to guard isolate.

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

Copy the mathematical state (left, right and sign) of another equation into this one. Entry point used by the constructor for an Equation input.

Get the degree of the equation

Divide both members of the equation by a value (coerced to a Fraction). A zero divisor is a no-op (the equation is returned unchanged). For an inequality, a negative divisor reverses the sign.

8x+10=6x | 2  ->  4x+5=3x
Copy

Evaluate the equation as a predicate: substitute the given variable values into both members and return whether the relation left <sign> right holds (the equation sign is honoured, including inequalities). Distinct from the value-producing evaluate of Polynom/Monom (which returns a number).

Whether the equation contains a cross-term monom (a single monom carrying more than one variable, such as xy), which prevents isolating a variable linearly. A linear equation in several distinct variables (e.g. ax+by+c=0) has no cross-term and stays isolable.

Determine if the equation contains a variable.

Strict equality: both members are identical as written and the sign matches. Sensitive to how terms are split and to the side order (3x=5 is not isEqual to 5=3x). For "same solutions", use isEquivalentTo.

Equivalence: the two (in)equations share the same solution set. All terms are moved left and the resulting polynoms are compared up to a scalar factor (3x=5, 3x-5=0 and 6x=10 are all equivalent). For inequalities a negative factor mirrors the equation, so the sign must reverse accordingly. Looser than isEqual.

Reorder the equation to keep a single variable on the left and the rest on the right, with a coefficient of 1. For an inequality, a negative coefficient reverses the sign. Atomic: on failure the receiver is left unchanged.

Reorder will move all monoms containing a variable on the left, all the other on the right.

Multiply both members of the equation by one or more fraction values. A negative factor reverses the inequality sign. Atomic: a failing operand leaves the receiver intact.

Multiply both members by -1. For an inequality the direction is reversed (x < 3 becomes -x > -3), so the equation keeps the same solutions.

Router: dispatch an input to the matching from*** method. A same-type input goes through copy, a string is a full equation (strict: fromString throws if it carries no sign), and a bare algebraic expression is read as <expr> = 0.

Raise both members to the power value. The sign is left as it is, so squaring an inequality does not keep its solutions.

Put the equation in a canonical form: every term on the left (the right member is zero), integer coefficients without common divisor, and a positive leading coefficient. A negative factor reverses the sign of an inequality.

Move the terms with a variable to the left and the constants to the right. With allLeft, move everything to the left instead. The sign does not change.

Replace a variable by a polynom in both members (in place).

Multiply by the lcm denominator and divide by the gcm numerators.

Solve left - right = 0, whatever the sign, and return the roots as Solutions sorted by value. An inequality has the roots of its equality: use TableOfSigns to study its sign.

Copies of the left and right members, as [left, right].

Subtract one or more values from the equation (member by member for an Equation operand, from both members otherwise). Atomic: a failing operand leaves the receiver intact.

True when both members have the same value for the given values of the variables. The sign is ignored: use evaluate to test an inequality.

Build the equation from its two members and an optional sign (defaults to =).

Build the equation from a complete equation string (containing a sign).

True when the string contains an equation sign (=, < or >).

Remove the duplicated solutions (same tex), keeping the first one. With sorted, sort them by value.