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Name

Example

Description

+, -, *, /,^ or **

3.5*3+3/(4-5^2)

Elementary math.

Name of object

AB/CD

The name of a segment, circle, angle and other expression. The object
must not depend on the current object. To refer to objects
by name there is the syntax @name or @"name". This will not work in
macros, however. If the object is not found, an error will occur.

Function

sin(a)

The functions abs, sign, sin, cos, tan, arcsin, arccos, arctan, sqrt,
exp, log, round, ceil, floor, deg, rad, sinhyp, coshyp, angle180 and angle360. Note
that the trigonometric functions work with degrees. To convert, use
deg(x), or the functions rsin, rcos, rtan, rarcsin, rarccos, rarctan.

User **Functions**

f(a)

Evaluation of a user defined function object at a.

**Pi **

pi

The constant Pi.

**x**,**y**,**z**

x(P), y(P) , z(P)

x- and y-coordinates of a point, or the z-value of the point.

**d**

d(P,Q)

Distance of two points.

**d**

d(x)

Computes changes of the expression x. If x is a point, it computes
movements.

**sum**

sum(x,f)

Sums up x. If f is negative or invalid, the sum is reset to 0.

**a**

a(P,Q,Z)

Size of angle PQZ.

**scale**

scale(x,a,b)

The relative position of x in [a,b), if x is in that interval. Else
the expression becomes invalid.

**if **

if(e,e1,e2)

Returns e1, if e is valid, else e2.

**invalid**

invalid Returns an invalid expression.

&&,||,! !

(x<4 && y<4)

Logical expressions. 1 is true, 0 is false.

<, >, <=, >=, ==, ~=

x<y

Comparing numbers. ~= means "circa equal".

**integrate**

integrate(f,a,b)

integrate(f)

Integrates the function f from a to b using the Romberg method. f
must be a function object (probably hidden). The y-part of f is
used. If f shows points only, the Riemann sum is computed. If f
is parametric, the area inside the curve is approximated or
its length, if it is not filled.

**zero**

zero(f,a,b)

Find a zero of the function f in the interval a,b. The sign of f
in a and b must be different. The procedure uses the secant method
or interval bisection.

**diff**

diff(f,a)

Numerically differentiate f at a. This is the usual approximation
(f(h)-f(-h))/(2h)

**min**,**max**

min(f,a,b)

Computes the point of the minimum (maximum) of f between a and b.
min(a,b) and max(a,b) compute the minimum or maximum of a and b.

**this**

x(this)

Refers to the object containing the expression.

**windoww**,**windowh**,**windowcx**,**windowcy**

Returns the dimensions and center coordinates of the current screen.

**pixel**

Returns the pixel per coordinate unit. Not to be used in print.

**simulate**

simulate(e,x,f)

Sets the expression e to to the value x, recomputes the construction with
this new value and returns the value of f. Only one simulation can be
computed at any time, so simulations can not be nested. An expression,
a fixed angle or a fixed circle can be used for e.

**inside**

inside(P,A)

Tests, if the point P is inside the object A. Returns 1/2, if it is
on the boundary if A. A can be a polygon, a circle or an angle.

**quad**

quad(a)

Computes a*a. These are the **quadrances** in **Rational Geometry**.

**spread**

s(t)

Compute sin(t)^2. These are the **spreads** in

**Rational Geometry**.

Related topics: Fixed angles, Fixed Circles, Points, Object Properties, Reorder points, Functions and Curves

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