Exact generators

The Exact collection

.Exact is an ordinary RiX map containing canonical symbolic generators:

Runnable RiXRun cell

pi := .Exact[:pi]; sqrt2 := .Exact[:sqrt2]; {: 3*pi, 1 + 2*sqrt2 }

The concise form again means lookup and multiplication:

Runnable RiXRun cell

explicit := 3/2 * .Exact[:pi]; concise := 3/2~{pi}; explicit == concise

Unlike a floating approximation, these remain exact expressions.

Algebraic relations

Algebraic generators carry a monic minimal polynomial. RiX reduces powers by that relation:

Runnable RiXRun cell

iSquared := .Exact[:i]^2; rootSquared := .Exact[:sqrt2]^2; {: iSquared, rootSquared }

The results are exactly -1 and 2.

Exact algebraic division

RiX can invert an expression in one algebraic extension:

Runnable RiXRun cell

a := 1 / .Exact[:i]; b := 1 / (1 + .Exact[:sqrt2]); {: a, b }

This produces -i and -1 + sqrt2. A sum involving a transcendental generator, such as 1 + pi, is not currently inverted automatically.

Exact physical magnitudes

Exact expressions can be quantity magnitudes:

Runnable RiXRun cell

halfTurn := 1/2~{pi}~[rad]; diameter := 2~[m]; halfTurn * diameter

The π factor and the physical dimensions remain distinct layers.

Define an algebraic generator

Polynomial coefficients are listed from constant term upward:

Runnable RiXRun cell

sqrt3 := .DefineExactGenerator(:sqrt3, [-3, 0, 1]); Exact := .Exact.Merge({= sqrt3=sqrt3 }); 1~{sqrt3}^2

Next

Complex numbers use the same exact-expression engine. The .Complex map adds conjugation and component operations without introducing approximate trig.