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Locus

Another exclusive Foundation RISCWorld application

Appendix A - Formula Input.

Variables

Formula input is dependant on the plotting mode you are in, but the preset functions available are the same even when the variables used differ and are as follows.

Mode	Independent variable	Dependent variable
Cartesian	x	y
Cartesian parametric	t	x. y
Polar	t	r
Polar parametric	t	r, �
Implicit	x, y

For example: In parametric mode the equations -

    x=cost
    y=sint

would be written as -

    cost,sint.

You do not need to type the 'y=' or 'r=' as this is assumed by Locus. The appropriate dependent variables are automatically placed in the icon to the immediate left of the formula input icon.

In implicit mode nothing will appear in this icon as it is up to the user to enter the entire equation.

Available Functions

Locus has a number of preset functions built in including a complete set of trigonometric functions and hyperbolic trig functions plus some other useful common functions.

An additional function is 'blanc', which draws the blancmange function. This is continuous everywhere and differentiable nowhere and is very useful in teaching calculus as nowhere is it locally straight. If you are interested you could also try plotting 'r=blanct' in polar mode.

These functions can be entered in standard mathematical notation as Locus will add any required brackets. For example, typing 'asinx' in the formula input icon will plot the graph of y=asinx by replacing 'asinx' with the name of the function FN_ARCSIN(X) which will then be evaluated.

If there is the possibility of ambiguity the user should use appropriate sets of brackets. For example. if you were writing a transformation matrix for a data set to perform a rotation of PI/4 radians about the origin then the matrix should include brackets around the constant value because Locus will interpret 'cosp/4' as (COS(PI))/4, which will result in a rotation of PI radians and an enlargement scale factor 0.25. Instead the matrix should be written as follows:

Please note that the Implicit plotting routines are at an embryonic stage at the time of writing and while they are capable of dealing with simple functions like one-to-one mapping (e.g. 4x-3y=-7 or xy=10) and some two-to-one and one-to-two mappings, Locus will plot rubbish if asked to deal with most many-to-many mappings and any trigonometric input. I have included this basic Implicit capacity because it is very useful for teaching simultaneous linear equations.

Foundation RISCWorld