Syntax of Terms

Terms are specified in normal, usual mathematical syntax. Yet there are some points, which should be noted:

  • Blanks inside terms are ignored
  • Terms are noted case-sensitive … sin(x) ≠ Sin(x)

Primitives

Numbers

  • 0 | 5 | 12 | 1024 | ...
  • 3.14 | 2.718 | 0.5
  • Not Supported: 3,14 | .5 | 1e6

Parameters

  • e
  • pi | π
  • inf | ∞

Variables

  • a | b | c | d | e | f | g | h | i | j | k | l | m | n | o | p | q | r | s | t | u | v | w | x | y | z

Not interpreted as a variable

  • e | i | o

Using parameters notations or strings longer than 1 letter as variables

  • var(<string>)

Examples

  • var(e)
  • var(area)

Operations

List of Operations

  • +
  • *
  • /
  • ^

Operation Priority (from highest to lowest)

  • ^
  • /
  • *
  • + | –

Examples

  • a+b*c = a+(b*c) | (≠ (a+b)*c)
  • a*b/c = a*(b/c) | (≠ (a*b)/c)
  • a^b*c = (a^b)*c | (≠ a^(b*c))
  • a*b^c = a*(b^c) | (≠ (a*b)^c)
  • a/b^c = a/(b^c) | (≠ (a/b)^c)

Note: Use “( )” to avoid implicit prioritization of operations

Left / Right associativity

  • / will be interpreted from left to right
  • ^ will be interpreted from right to left

Examples

  • a/b/c = (a/b)/c | (≠ a/(b/c))
  • a^b^c = a^(b^c) | (≠ (a^b)^c)

Implicit Multiplication

Missing operations will be interpreted as *

Examples

  • 2a = 2*a
  • x(x+1)(x+2) = x*(x+1)*(x+2)
  • xy^2z = x*y^2*z
  • abchjxy = a*b*c*h*j*x*y

Note: Predefined syntax-constructs will not be separated into products

  • sin(x) ≠ s*i*n*(x)
  • 25 ≠ 2*5
  • pi ≠ p*i

Functions

Functions are generally notated as

  • <name>(<argument>) | <name><argument> topic =<Topic>
  • <name>(<argument1>) | <argument2> | …)

Note: sinx+y ≠ sin(x+y)

Note: sin[x] is not defined

Function Names

  • ln
  • log
  • sqrt | √
  • sin
  • cos
  • tan
  • asin | sin^-1
  • acos | cos^-1
  • atan | tan^-1

Examples

  • ln(x) or log(x)
  • log(2,8) // logarithm of 8 to the base of 2
  • sqrt(2) or √(2) or √2
  • sqrt(3,8) or √(3,8) // 3-th root of 8
  • sin(x+2π) | cos(x) | tan(x+y)
  • asin(3x+1) | sin^-1(3x)

Function Power Notation

The notation <name>^n(<argument>) is supported for n ≥ 2

Examples

  • ln^5(x) = ln(x)^5 (≠ ln(x^5))
  • sin^2x+cos^2x = sin(x)^2+cos(x)^2

Note: sin^-1(x) ≠ sin(x)^-1

Equations and Inequations

Equation, Comparison Signs

  • =
  • >
  • >= | ≥
  • <
  • <= | ≤

Examples

  • (x+1)/x=x
  • 3x+1=3-x
  • x^2>=4 or x^2≥4
  • -x+4<5

The single equations of a given system of equations are separated by ‘;’

Examples for system of equations

  • x+y=2; x-y=5
  • x+y+z=3; y+z=2; z=x+5y-7

Derivation

Implicit Notation

  • (<expression>)’ or <expression>’

The unknown can be specified in the settings – or will be automatically set to x

Examples

  • (x*(x+1))’ (≠ x*(x+1)’)
  • sin(x)’ (don’t write sinx’)

Explicit Notation

  • der(<expression>, <variable>)

Examples

  • der(cos(x)sin(y),x) // Derivation for x
  • der(cos(x)sin(y),y) // Derivation for y

Integrals

  • ∫(<expression>,<variable>) or int(<expression>,<variable>)

Examples

  • int(sin(x)cos(x),x)
  • int(3e^y,y)

Definite Integral

  • ∫(<lowerlimit>,<upperlimit>,<expression>,<variable>) or int(<lowerlimit>,<upperlimit>,<expression>,<variable>)

Examples

  • int(0,1,x^2,x)
  • int(π/4,π/2,sin(y),y)