CAS View

From GeoGebra Manual
Revision as of 10:38, 2 August 2011 by Andrea.duringer (talk | contribs)
Jump to: navigation, search


Basic input

  • Enter: evaluate input
  • Ctrl+Enter: check input but do no evaluate input, e.g. b+b stays b+b. Note that assignments are always evaluated, e.g. a := 5
  • In an empty row type
    • space bar for previous output
    • ) for previous output in parentheses
    • = for previous input
  • Suppress output with a semicolon at the end of your input, e.g. a := 5;

Toolbar

  • Clicking a button in the toolbar applies a command to the currently edited row
  • You can select part of the input text to only apply the operation to this selected part

Variables

Assignments & Connection with GeoGebra

  • Assignments use the := notation, e.g. b := 5, a(n) := 2n + 3
  • To free up a variable name again, use Delete[b] or b :=
  • Variables and functions are always shared between the CAS view and GeoGebra if possible. If you define b:=5 in the CAS view, then you can use b in all of GeoGebra. If you have a function f(x)=x^2 in GeoGebra, you can also use this function in the CAS view.

Row References

You can refer to other rows in the CAS view in two ways

  • Static row references insert text from another row, so your input is changed.
    • # inserts the previous output
    • #5 inserts the output of row 5
    • ## inserts the previous input
    • #5# inserts the input of row 5
  • Dynamic row references use text from another row, but don't change your input.
    • $ inserts the previous output
    • $5 inserts the output of row 5
    • $$ inserts the previous input
    • $5$ inserts the input of row 5

Equations

  • Equations are written using the simple Equals sign, e.g. 3x + 5 = 7
  • You can perform arithmetic operations on equations, e.g. (3x + 5 = 7) - 5 subtracts 5 from both sides of the equation. This is useful for manual equation solving.
  • LeftSide[3x + 5 = 7] gives 3x+5 and RightSide[3x + 5 = 7] gives 7

Solve Equations

You can use the Solutions and Solve commands to solve equations.

  • Solutions[ equation ] solves an equation for x
    • Solutions[ x^2 = 4 ] returns {2, -2}
  • Solutions[ equation, var ] solves an equation for the given variable.
    • Solutions[ 3a = 5b, a ] returns {5b / 3}
  • Solve[ equation ] solves an equation for x
    • Solve[ x^2 = 4 ] returns {x = 2, x = -2}
  • Solve[ equation, var ] solves an equation for the given variable.
    • Solve[ 3a = 5b, a ] returns {a = 5b / 3}

System of Two Equations

  • Solutions[{equation1, equation2}] solves two equations for x and y
    • Solutions[{x + y = 2, y = x}] returns {{1,1}}
  • Solutions[{equation1, equation2},{var1, var2}] solves two equations for var1 and var2
    • Solutions[{a + b = 2, a = b}, {a, b}] returns {{1,1}}
  • Solve[{equation1, equation2}] solves two equations for x and y
    • Solve[{x + y = 2, y = x}] returns {{x = 1, y = 1}}
  • Solve[equation1, equation2, var1, var2] solves two equations for var1 and var2
    • Solve[{a + b = 2, a = b}, {a, b}] returns {{x = 1,y = 1}}

Basic commands

  • Expand[ exp ]expands the given expression
    • Expand[ (x-2) (x+3) ] returns x^2 + x - 6
  • Factor[ exp ] factors the given expression
    • Factor[ 2x^3 + 3x^2 - 1 ] returns 2*(x+1)^2 * (x-1/2)
  • Numeric[ exp ], Numeric[ exp, precision ] tries to determine a numerical approximation of the given expression
    • Numeric[ 1/2 ] returns 0.5
    • Numeric[ sin(1), 20 ] returns 0.84147098480789650666

Calculus

  • Limit[ exp, var, value ] tries to determine the limit of an expression.
    • Limit[ sin(x)/x, x, 0 ] returns 1
  • LimitAbove[ exp, var, value ] tries to determine the limit of an expression.
    • LimitAbove[ 1/x, x, 0 ] returns Infinity
  • LimitBelow[ exp, var, value ] tries to determine the limit of an expression.
    • LimitBelow[ 1/x, x, 0 ] returns -Infinity
  • Sum[ exp, var, from, to ] finds the sum of a sequence
    • Sum[i^2, i, 1, 3] returns 14
    • Sum[r^i, i,0,n] returns (1-r^(n+1))/(1-r)
    • Sum[(1/3)^i, i,0,Infinity] returns 3/2
  • Derivative[ function ], Derivative[ function, var ], Derivative[ function, var, n ] takes the derivative of a function with respect to the given variable. If no variable is given, "x" is used.
    • Derivative[ sin(x)/x^2, x ] returns (x^2*cos(x) - sin(x)*2*x) / x^4
    • Derivative[ sin(a*x), x, 2 ] returns -sin(a*x)*a^2
  • Integral[ function, var ], Integral[ function, var, x1, x2 ] finds the (definite) integral of a function with respect to the given variable
    • Integral[ cos(x), x ] returns sin(x)
    • Integral[ cos(x), x, a, b ] returns sin(b) - sin(a)

Further Commands and Tools

For the complete list see CAS Commands and CAS tools.

© 2021 International GeoGebra Institute