⇨ USER INTERFACE:

→ Click on the [HELP] button to display (or hide) this help. Type help in the input field for the same action.
→ Click on the [CLEAR] button to clear the results area. Type clear in the input field for the same action.
→ Click on the [LIST DEF] button to list the defined functions/variables/equations. Type listdef in the input field for the same action.
→ Click on the [CLEAR DEF] button to clear the defined functions/variables/equations. Type cleardef in the input field for the same action.
→ Click on the [STEP BY STEP] button to enable/disable the steps in any computation. Type stepbystep or sbs in the input field for the same action.

⇨ MATHS FEATURES:

 Generalities:
→ The following maths operators/functions/symbols are supported: * · × + - / ^ () {} [] , ; ' " ° i e pi cos sin tan ln log exp sqrt abs acos arccos asin arcsin atan arctan coord mod norm ∅ +∞ -∞ ℝ ∪ π
→ i, e and pi are specific constants: i is the imaginary unit: "sqrt(-1)", e is the Euler's constant (~2.72) and pi is the pi constant (~3.14)
→ For numeric results, the displayed precision is 4 digits while the internal precision is around 15-20 digits. Rounded numbers are prefixed by ~
→ Variables can be optionnally named with up to two letters then optionally an underscore, then up to two digits and finally up to two quotes. Examples: x, eq1, F2, g'', un_1, etc.
→ After computation, the last result is stored in the res variable while the numeric value of the result (if it exists) is stored in the num variable.
→ For differentiation, integration, resolution and factorization, you may specify the variable(s) used for the operation. If none is specified, the variable is picked up in the math expression (taking the following order into account: x, y, z, a, b and c).
→ While $0^0$ may be indeterminate, it returns 1 in computation.
→ $\log (b,v)$ is the logarithm function of base b, it is converted into: $\frac{\ln \left(v\right)}{\ln \left(b\right)}$

 Define:
→ Use = (equals) or : (colon) to define a variable, function, equation/inequality or sequence.
  Examples:
   J=1.2345 defines the variable J as 1.2345
   f(x)=4*x+8 defines the fonction f as $4x+8$
   eq1: 7*x-1>0 defines the equation eq1 as $7x-1>0$
   u(n)=4n/(3n+1) defines the sequence u(n) as $\frac{4n}{3n+1}$
→ The sequence can be defined in a recursive way and a specific beginning value can be then set.
  Example:
   v(n+2)=v(n+1)-v(n) defines the sequence v(n) as v(n + 1) - v(n) then v(0)=1 sets the value v(0) as 1

 Apply:
→ Use a function with a value between parenthesis to apply a value to a function.
  Examples:
   f(4) returns 24 if the function f has been defined as f(x) = 4*x + 8
   f(1,2) returns 8 if the function f has been defined as f(x,y) = 2*x + 3*y
   f(y=1) returns $2x+3$ for the same function f

 Calculate:
→ Use the calc keyword to compute the result of a math expression. This is the default function used if none has been defined.
  Examples:
   calc(4*8) returns 32
   4*8 also returns 32 as calc is used by default
   (1+e)^2 returns $e^2+2e+1$
→ calc is mostly a combination of the simplify function (for simplification) and the expand function (for expanding an expression).
  Differences:
   (1+x)^3/(1+x) or calc((1+x)^3/(1+x)) returns $x^2+2x+1$
   simplify((1+x)^3/(1+x)) returns ${(x+1)}^2$
   expand((1+x)^3/(1+x)) returns $\frac{x^3+3x^2+3x+1}{x+1}$
→ When a numeric value can be computed from the result, it is also returned.

 Differentiate:
→ Use the diff keyword to differentiate a math expression.
  Example:
   diff(4*x+cos(x)) returns $-\sin \left(x\right)+4$

 Solve:
→ Use the solve keyword to solve a math equation/inequality (in ℝ).
  Examples:
   solve(4*x^2=8) returns $x=\{-\sqrt{2},\sqrt{2}\}$
   solve(2*x>3,x) returns $x\in ]\frac{3}{2},\mathrm{+\infty }[$. The x argument defines the variable used for the resolution
→ Multiple equations can be solved at the same time when passed as multiple arguments.
  Examples:
   solve({a+b=4,a-2*b=1}) or solve({a+b=4,a-2*b=1},{b,a}) returns $\{a=3,b=1\}$

 Factorize:
→ Use the factor keyword to factorize a math expression or an integer.
  Examples:
   factor(4*x+8) returns $4·(x+2)$
   factor(27880) returns $2^3·5·17·41$
→ As this feature forcefully adds fractions, it can be directly used for that purpose.
  Example:
   factor(1+1/(2*x+1)) returns $\frac{2·(x+1)}{2x+1}$

 Integrate:
→ Use the integ keyword to integrate a math expression with or without an interval.
  Examples:
   integ(4*x+8) returns $2x^2+8x+C$
   integ(x^2,x,[a,b]) returns $\frac{-a^3+b^3}{3}$

 Trigonometry:
→ cos, sin and tan are the trigonometric functions: cosine, sine and tangent.
→ acos, asin and atan are their inverses.
  Examples:
   cos(Pi/4) returns $\frac{\sqrt{2}}{2}$
   acos(sqrt(2)/2) returns $\frac{\pi }{4}$
→ By default, values are in radians but can be considered as degrees using the ° sign.
  Examples:
   cos(45°) returns $\frac{\sqrt{2}}{2}$
   acos°(sqrt(2)/2) returns 45

 Geometry:
→ Use the coord keyword to define any point, vector or line segment. Then, you can "add", "multiply" or "divide" coordinates.
  Examples:
   coord(1,2)+coord(3,4) returns $\mathrm{coord}(4,6)$ (like a translation)
   coord(1,2)*coord(3,4) returns $11$ (dot product)
   coord(1,2)/2 returns $\mathrm{coord}(\frac{1}{2},1)$ (midpoint of a segment)
→ Use the norm keyword to compute the (euclidian) norm of the coordinates.

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