WIP #300 improve getting started markdown doc

symja_android_library/doc/01-getting-started.md

@@ -1,5 +1,5 @@
 
-- [Basic calculations](#basic-calculations) 
+- [Basic calculations](#basic-calculations)
 - [Tutorial](#tutorial) 
 - [Reference](#reference) 
 
@@ -9,6 +9,7 @@ Symja can be used to calculate basic stuff:
 
 ```
 >> 1 + 2
+3
 ```
 
 To submit a command to Symja, press Shift+Return in the Web interface or Return in the console interface. The result will be printed in a new line below your query.
@@ -17,12 +18,14 @@ Symja understands all basic arithmetic operators and applies the usual operator
 
 ```
 >> 1 - 2 * (3 + 5) / 4
+-3
 ```
 
 The multiplication can be omitted:
 
 ```
 >> 1 - 2 (3 + 5) / 4
+-3
 ```
 
 But function `f(x)` notation isn't interpreted as `f*(x)`
@@ -31,22 +34,25 @@ But function `f(x)` notation isn't interpreted as `f*(x)`
 >> f(x)
 ```
 
-Powers expressions like ${3}^{4}$ can be entered using `^`:
+Powers expressions like ${3}^{4}$ can be entered using ^:
 
 ```
 >> 3 ^ 4
+81
 ```
 
 Integer divisions yield rational numbers like $\frac{6}{4}$ :
 
 ```
 >> 6 / 4
+3/2
 ```
 
 To convert the result to a floating point number, apply the function `N`:
 
 ```
 >> N(6 / 4)
+1.5
 ```
 
 For integer number bases other than `10` the `^^` operator can be used. Here's an example for a hexadecimal number:
@@ -60,93 +66,117 @@ The number can be converted back to hexadecimal form with the `BaseForm` functio
 
 ```
 >> BaseForm(2882400255, 16)
+Subscript[abcdefff,16]
 ```
 
-As you can see, functions are applied using the identifier `N` and parentheses `(` and `)`. 
-In general an identifier is a user-defined or built-in name for a variable, function or constant. 
+### Symbols with upper and lower case characters
+
+Functions are applied using an identifier and parentheses `(` and `)`. 
+In general an identifier is a user-defined or built-in name for a variable, function or constant.
+
 Only the identifiers which consists of only one character are case sensitive. 
 For all other identifiers the input parser doesn't distinguish between lower and upper case characters.
 
 For example: the upper-case identifiers [D](functions/D.md), [E](functions/E.md), [I](functions/I.md), [N](functions/N.md), 
-are different from the identifiers `d, e, i, n`, whereas the 
-functions like [Factorial](functions/Factorial.md), [Integrate](functions/Integrate.md) can be entered as 
-`factorial(100)` or `integrate(sin(x),x)`. If you type `SIN(x)` or `sin(x)`, 
-Symja assumes you always mean the same built-in [Sin](functions/Sin.md) function.  
+are different from the identifiers `d, e, i, n`, whereas the functions like [Factorial](functions/Factorial.md), [Integrate](functions/Integrate.md) can be entered as `factorial(100)` or `integrate(sin(x),x)`. 
+If you type `SIN(x)` or `sin(x)`, Symja assumes you always mean the same built-in [Sin](functions/Sin.md) function.  
 
-Symja provides many common mathematical functions and constants, e.g.:
+Symja provides many common mathematical functions and constants.
+
+For example `[Log](functions/Log.md)` calculates the natural logarithm for base `[E](functions/E.md)`. `[Log2](functions/Log2.md)` and `[Log10](functions/Log10.md)` are variants for logarithm to the bases `2` and `10`.
 
 ```
 >> Log(E)
+1
 
 >> Sin(Pi)
+0
 
 >> Cos(0.5)
+0.877583
 ```
 
 When entering floating point numbers in your query, Symja will perform a numerical evaluation and present a numerical result, pretty much like if you had applied N.
 
+### Complex numbers
+
 Of course, Symja has complex numbers and uses the equation:
 
 $$\sqrt{-1}=I$$
 
-In Symja the imaginary unit is represented by the uppercase letter `I`:
+In Symja the imaginary unit is represented by the uppercase letter `[I](functions/I.md)`:
 
 ```
 >> Sqrt(-4)
+2*I
 
 >> I ^ 2
+-1
 
 >> (3 + 2*I) ^ 4
+-119+I*120
 
 >> (3 + 2*I) ^ (2.5 - I)
+43.663+I*8.28556
 
 >> Tan(I + 0.5)
+0.195577+I*0.842966
 ```
 
-`Abs` calculates absolute values:
+`[Abs](functions/Abs.md)` calculates absolute values for complex numbers:
 
 ```
 >> Abs(-3)
+3
 
 >> Abs(3 + 4*I)
+5
 ```
 
 Symja can operate with pretty huge numbers:
 
 ```
 >> 100!
+9332621544394415268169923885626670049071596826438162146859296389521759999322991\
+5608941463976156518286253697920827223758251185210916864000000000000000000000000
 ```
 
 (! denotes the factorial function.) The precision of numerical evaluation can be set:
 
 ```
 >> N(Pi, 100)
+3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067
 ```
 
-Division by zero is forbidden:
+Division by zero is forbidden and prints the message `Power: Infinite expression 1/0 encountered.`
 
 ```
 >> 1 / 0
+ComplexInfinity
 ```
 
 Other expressions involving `Infinity` are evaluated:
 
 ```
->> Infinity + 2 Infinity
+>> Infinity + 2*Infinity
+Infinity
 ```
 
-In contrast to combinatorial belief, ${0}^{0}$ is undefined:
+In contrast to combinatorial belief, `{0}^{0}` is undefined and prints the message `Power: Indeterminate expression 0^0 encountered.`:
 
 ```
 >> 0 ^ 0
+Indeterminate
 ```
 
 The result of the previous query to Symja can be accessed by %:
 
 ```
 >> 3 + 4
+7
 
 >> % ^ 2
+49
 ```
 
 In the console available functions can be determined with the `?` operator

symja_android_library/matheclipse-core/src/main/resources/doc/01-getting-started.md

@@ -1,5 +1,5 @@
 
-- [Basic calculations](#basic-calculations) 
+- [Basic calculations](#basic-calculations)
 - [Tutorial](#tutorial) 
 - [Reference](#reference) 
 
@@ -9,6 +9,7 @@ Symja can be used to calculate basic stuff:
 
 ```
 >> 1 + 2
+3
 ```
 
 To submit a command to Symja, press Shift+Return in the Web interface or Return in the console interface. The result will be printed in a new line below your query.
@@ -17,12 +18,14 @@ Symja understands all basic arithmetic operators and applies the usual operator
 
 ```
 >> 1 - 2 * (3 + 5) / 4
+-3
 ```
 
 The multiplication can be omitted:
 
 ```
 >> 1 - 2 (3 + 5) / 4
+-3
 ```
 
 But function `f(x)` notation isn't interpreted as `f*(x)`
@@ -35,18 +38,21 @@ Powers expressions like ${3}^{4}$ can be entered using ^:
 
 ```
 >> 3 ^ 4
+81
 ```
 
 Integer divisions yield rational numbers like $\frac{6}{4}$ :
 
 ```
 >> 6 / 4
+3/2
 ```
 
 To convert the result to a floating point number, apply the function `N`:
 
 ```
 >> N(6 / 4)
+1.5
 ```
 
 For integer number bases other than `10` the `^^` operator can be used. Here's an example for a hexadecimal number:
@@ -60,93 +66,117 @@ The number can be converted back to hexadecimal form with the `BaseForm` functio
 
 ```
 >> BaseForm(2882400255, 16)
+Subscript[abcdefff,16]
 ```
 
-As you can see, functions are applied using the identifier `N` and parentheses `(` and `)`. 
-In general an identifier is a user-defined or built-in name for a variable, function or constant. 
+### Symbols with upper and lower case characters
+
+Functions are applied using an identifier and parentheses `(` and `)`. 
+In general an identifier is a user-defined or built-in name for a variable, function or constant.
+
 Only the identifiers which consists of only one character are case sensitive. 
 For all other identifiers the input parser doesn't distinguish between lower and upper case characters.
 
 For example: the upper-case identifiers [D](functions/D.md), [E](functions/E.md), [I](functions/I.md), [N](functions/N.md), 
-are different from the identifiers `d, e, i, n`, whereas the 
-functions like [Factorial](functions/Factorial.md), [Integrate](functions/Integrate.md) can be entered as 
-`factorial(100)` or `integrate(sin(x),x)`. If you type `SIN(x)` or `sin(x)`, 
-Symja assumes you always mean the same built-in [Sin](functions/Sin.md) function.  
+are different from the identifiers `d, e, i, n`, whereas the functions like [Factorial](functions/Factorial.md), [Integrate](functions/Integrate.md) can be entered as `factorial(100)` or `integrate(sin(x),x)`. 
+If you type `SIN(x)` or `sin(x)`, Symja assumes you always mean the same built-in [Sin](functions/Sin.md) function.  
 
-Symja provides many common mathematical functions and constants, e.g.:
+Symja provides many common mathematical functions and constants.
+
+For example `[Log](functions/Log.md)` calculates the natural logarithm for base `[E](functions/E.md)`. `[Log2](functions/Log2.md)` and `[Log10](functions/Log10.md)` are variants for logarithm to the bases `2` and `10`.
 
 ```
 >> Log(E)
+1
 
 >> Sin(Pi)
+0
 
 >> Cos(0.5)
+0.877583
 ```
 
 When entering floating point numbers in your query, Symja will perform a numerical evaluation and present a numerical result, pretty much like if you had applied N.
 
+### Complex numbers
+
 Of course, Symja has complex numbers and uses the equation:
 
 $$\sqrt{-1}=I$$
 
-In Symja the imaginary unit is represented by the uppercase letter `I`:
+In Symja the imaginary unit is represented by the uppercase letter `[I](functions/I.md)`:
 
 ```
 >> Sqrt(-4)
+2*I
 
 >> I ^ 2
+-1
 
 >> (3 + 2*I) ^ 4
+-119+I*120
 
 >> (3 + 2*I) ^ (2.5 - I)
+43.663+I*8.28556
 
 >> Tan(I + 0.5)
+0.195577+I*0.842966
 ```
 
-`Abs` calculates absolute values:
+`[Abs](functions/Abs.md)` calculates absolute values for complex numbers:
 
 ```
 >> Abs(-3)
+3
 
 >> Abs(3 + 4*I)
+5
 ```
 
 Symja can operate with pretty huge numbers:
 
 ```
 >> 100!
+9332621544394415268169923885626670049071596826438162146859296389521759999322991\
+5608941463976156518286253697920827223758251185210916864000000000000000000000000
 ```
 
 (! denotes the factorial function.) The precision of numerical evaluation can be set:
 
 ```
 >> N(Pi, 100)
+3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067
 ```
 
-Division by zero is forbidden:
+Division by zero is forbidden and prints the message `Power: Infinite expression 1/0 encountered.`
 
 ```
 >> 1 / 0
+ComplexInfinity
 ```
 
 Other expressions involving `Infinity` are evaluated:
 
 ```
->> Infinity + 2 Infinity
+>> Infinity + 2*Infinity
+Infinity
 ```
 
-In contrast to combinatorial belief, ${0}^{0}$ is undefined:
+In contrast to combinatorial belief, `{0}^{0}` is undefined and prints the message `Power: Indeterminate expression 0^0 encountered.`:
 
 ```
 >> 0 ^ 0
+Indeterminate
 ```
 
 The result of the previous query to Symja can be accessed by %:
 
 ```
 >> 3 + 4
+7
 
 >> % ^ 2
+49
 ```
 
 In the console available functions can be determined with the `?` operator