Difference between revisions of "CAS View"

Revision as of 09:37, 10 August 2011

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

Commands and Tools

For a complete list of commands and tools see CAS Commands and CAS tools.

@@ Line 44: / Line 44: @@
 * LeftSide[3x + 5 = 7] gives 3x+5 and RightSide[3x + 5 = 7] gives 7
-==Solve Equations==
+==Commands and Tools==
-You can use the Solutions and Solve commands to solve equations.
+For a complete list of commands and tools see [[CAS Commands]] and [[CAS tools]].
-* 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 <nowiki>{{1,1}} </nowiki>
-* Solutions[{equation1, equation2},{var1, var2}] solves two equations for var1 and var2
-**  Solutions[{a + b = 2, a = b}, {a, b}] returns <nowiki>{{1,1}} </nowiki>
-* Solve[{equation1, equation2}] solves two equations for x and y
-**  Solve[{x + y = 2, y = x}] returns <nowiki>{{x = 1, y = 1}} </nowiki>
-* Solve[equation1, equation2, var1, var2] solves two equations for var1 and var2
-**  Solve[{a + b = 2, a = b}, {a, b}] returns <nowiki>{{x = 1,y = 1}} </nowiki>
-==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]].