System Variables

System variables are special reserved variable names used by some of the commands internally. They exist outside the folder structure that the other variables are located in, so they can be accessed in the same way from any folder.

Unlike normal variables, which take between 1 and 10 bytes to reference, system variables always take up 2 bytes, no matter how long the name.

Graph Variables

Equation Variables

The equation variables contain the equations that get graphed for each graphing mode. They include:

  • y1(x)–y99(x) in function mode
  • xt1(t)–xt99(t) and yt1(t)–yt99(t) in parametric mode
  • r1(θ)–r99(θ) in polar mode
  • u1(n)–u99(n) and ui1–ui99 in sequential mode
  • z1(x,y)–z99(x,y) in 3D mode
  • y1'(t)–y99'(t) and yi1–yi99 in differential equation mode

Cursor Variables

The cursor variables include xc, yc, zc, tc, rc, θc and nc. Some of them are updated whenever the crosshair cursor is being moved around on the graph screen, and are especially useful with the Input command. However, the rules that determine which ones get updated are a little tricky:

  • xc and yc are always updated, regardless of any settings.
  • The rest get updated depending on graphing mode: zc for 3D mode, tc for parametric mode, rc and θc for polar mode, and nc for sequential mode.
  • In addition, rc and θc get updated even outside polar graphing mode, if the graph format is set to polar coordinates.

Window Variables

The window variables define the parameters of the graphing window - they are not only used for graphing, but also with point commands such as PtOn. The most basic of them are xmin, xmax, ymin, and ymax: these determine the lower and upper bounds of the window. There are also more advanced settings:

  • xscl and yscl determine the distance between tick marks on the axes, if the axes are enabled.
  • Δx and Δy determine the distance between two pixels next to each other. They are calculated automatically from xmin-ymax, but you can set them yourself (xmax and ymax will be adjusted to fit).
  • xfact and yfact determine the factor by which the window is stretched when you zoom in or zoom out.

Some window variables are specific to graphing mode:

  1. In function mode:
    • xres determines the number of pixels between sample points for graphs (a higher value means lower quality).
  2. In parametric mode:
    • tmin and tmax determine the range of the variable t when graphing.
    • tstep determines the increment of the t variable between two sample points on the graph (a higher value means lower quality).
  3. In polar mode:
    • θmin and θmax determine the range of the variable θ when graphing.
    • θstep determines the increment of the θ variable between two sample points on the graph (a higher value means lower quality).
  4. In sequential mode:
    • nmin and nmax determine the n values to evaluate at: u(nmin), u(nmin+1), …, u(nmax) will be evaluated.
    • plotStrt and plotStep determine the n values that actually get graphed: starting at plotStrt, and increasing by plotStep each time.
  5. In 3D mode:
    • zmin and zmax (similarly to xmin and xmax) control the upper and lower bounds of the graphing window, for the z coordinate.
    • zscl (similarly to xscl) controls the distance between tick marks on the z axis, if the axes are enabled.
    • zfact (similarly to xfact) controls the factor by which the z-coordinate is stretched when you zoom in or out.
    • xgrid and ygrid determine the resolution of the wireframe grid.
    • eyeθ, eyeφ, and eyeψ control the viewing angle (eyeθ is the angle with the x-axis, eyeφ is the angle with the z-axis, and eyeψ is a rotation around the resulting line of sight)
    • ncontours is the number of contours to graph.
  6. In differential equation mode:
    • t0 determines the t-value for the initial conditions.
    • tplot and tmax determine range of the variable t when graphing.
    • tstep determines the increment of the t variable between two sample points on the graph (a higher value means lower quality).
    • ncurves determines the number of solution curves drawn if you don't give an initial condition.
    • diftol (with the Runge-Kutta method) and Estep (with the Euler method) determine a step size for calculations.
    • fldres determines the number of columns for the slope field, if one is drawn.
    • dtime determines the point in time at which a direction field is drawn (if one is drawn at all).
    • fldpic is a picture variable that stores the slope field to avoid redrawing it if it's unnecessary.

Graph Zoom

Many of the above window variables have a zoom variable counterpart, prefixed with a z. These are saved by the ZoomSto and ZoomRcl commands.

Statistics Variables

Regression models

These variables are created when you calculate a curve to fit a set of data, using one of these commands: LinReg, MedMed, QuadReg, CubicReg, QuartReg, PowerReg, ExpReg, LnReg, or Logistic.

  • regeq(x) is the curve that was calculated, as a function of x.
  • regcoef is a list of the coefficients calculated.
  • corr is the correlation coefficient (a measure of the direction and goodness of fit) of a linear model.
  • R2 is the square of corr, but can be calculated for all models. A value close to 1 indicates a good fit; a value close to 0 is poor.
  • medx1, medx2, medx3, medy1, medy2, and medy3 are calculated by the MedMed method.

Sample Statistics

These variables are calculated by the OneVar and/or TwoVar commands (only those that deal with one variable are calculated by OneVar).

  • $\bar{x}$ and $\bar{y}$ are the averages of each data set.
  • Σx and Σy are the sums.
  • Σx2 and Σy2 are the sums of the squares.
  • Σxy is the sum of the products of matching pairs of the two data sets.
  • minX, maxX, minY, and maxY are the minimum and maximum.
  • Sx and Sy are the sample standard deviations.
  • σx and σy are the population standard deviations.
  • nStat is the number of elements in a data set.
  • medStat, q1, and q3 (for OneVar only) are the median, first quartile, and third quartile.

Other Variables

The rest of the variables don't fit into any of the above categories.

  • c1–c99 are columns in the last data variable shown in the Data/Matrix editor.
  • errornum contains an error code once an error has occured, for use in Try..Else..EndTry blocks.
  • eqn and exp are used by the numerical solver (the equation to be solved is stored in eqn, and this is set equal to exp if the = sign was omitted).
  • ok is set to 1. if a Dialog menu has been exited successfully, and 0. if it was exited with the ESC key.
  • seed1 and seed2 are the seeds for the random number generator used by rand().
  • sysData is the default data variable used by the BldData command.
  • sysMath stores the result of any graphing calculation (for example, for calculating the derivative at a point on the graph)
  • tblStart and Δtbl are used to calculate the table input when it is automatic.
  • tblInput stores the table input when it's not automatic.
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