Real numbers should be written without spaces.
If the number is a fraction, it should be given as a simple fraction, not a decimal fraction, e.g. the number \({1\over 4}\) should be written as 1/4, not 0.25.
The number \(\pi\) should be written as pi.
When entering arithmetic operations, only standard characters should be used: addition +, subtraction -, multiplication * and division /. Particular attention should be paid to multiplication. Omitting the * is one of the most common syntax mistakes.
Examples:
- \(3x\) should be written as
3*x, - \(x(ax+1)(x−1)\) should be written as
x*(a*x+1)*(x-1).
When entering algebraic expressions, use parentheses to specify the order of operations. Therefore, you need to think carefully about the form of the answer and put all the necessary brackets but avoid placing too many. Only round brackets, i.e. (,), should be used in algebraic expressions, even if they are nested. Brackets [,] and curly braces {,} are not allowed here because they have different meanings.
Examples:
-
(a+b)/(c+d)will be interpreted as \[{a+b\over c+d}\] -
a+b/c+dwill be interpreted as \[a+{b\over c}+d\] -
a/b/cora/(b*c)will be interpreted as \[{a\over bc}\] -
a/b*cwill be interpreted as \[{a\over b}\cdot c\]
Sets with a finite number of elements should be saved with braces
{, }.
Therefore, a set \(\{1,2,3\}\) should be saved as {1,2,3}.
The empty set \(\emptyset\) should be saved as {}.
Open and closed intervals should be written using round brackets
( , ) and angle brackets < , >.
If the endpoint is \(\infty\) or \(-\infty\), should be entered
oo (two lowercase o) or -oo (minus two lowercase o), respectively.
The set of real numbers \(\mathbb{R}\) should be written as an open interval (-oo,oo).
The sums of sets and intervals should be written using the three-letter cup shortcut instead of the symbol for the sum of sets \(\cup\).
The set difference symbol \ cannot be used. The given set should be saved as the sum of appropriate intervals. For example, the set \(\mathbb{R}\backslash\{1\}\) should be represented as \((-\infty,1)\cup(1,\infty)\) and should therefore be written as (-oo,1)cup(1,oo).
The coordinates of the points should be entered as an ordered pair of numbers, i.e. using parentheses and separating the numbers with a comma. For example, a point \((2,3)\) must be entered as (2,3).
The vector coordinates should be entered using square brackets and separated by numbers with a comma. For example, a vector \([3,-8]\) must be entered as [3,-8].
Use ^ (SHIFT + 6) to write powers, for example \(x^2\) should be entered as x^2. Powers with negative or fractional exponents require the use of parentheses.
Exercises:
- \(\displaystyle x^{-2}\) should be entered as
x^(-2), - \(\displaystyle x^{{1\over 3}}\) should be entered as
x^(1/3).
You can use the sqrt(x) command to write \(x^{1\over 2}\), i.e. \(\sqrt{x}\) remembering that round brackets are used.
To write a root of a degree other than \(2\), e.g. \(\root 6 \of {x}\) it must be represented in the form of power, i.e. x^(1/6).
Answers should use predefined functions whose arguments should be placed in parentheses (, ). Because the system is case-sensitive, it is important to use uppercase and lowercase letters consciously.
The square root function \(\sqrt{x}\) should be written as sqrt(x).
The logarithmic function \(\log_a x\) should be written as log(x,a).
Hence \(\log_2 7\) should be written as log(7,2) and \(\log x\) as log(x,10).
Trigonometric functions should be symbolically written as follows:
- \(\sin x\) –
sin(x), - \(\cos x\) –
cos(x), - \(\tan x\) –
tan(x), - \(\cot x\) –
cot(x).