diff --git a/symja_android_library/doc/01-getting-started.md b/symja_android_library/doc/01-getting-started.md index 37c67e61f0..e06ade4d58 100644 --- a/symja_android_library/doc/01-getting-started.md +++ b/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 diff --git a/symja_android_library/matheclipse-core/src/main/resources/doc/01-getting-started.md b/symja_android_library/matheclipse-core/src/main/resources/doc/01-getting-started.md index 3ee3532710..e06ade4d58 100644 --- a/symja_android_library/matheclipse-core/src/main/resources/doc/01-getting-started.md +++ b/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