Real calculation syntax

A calculus may use operators + (addition), - (subtraction), * (multiplication), / (division), ^ (power of a number), ² (square), (by priority decreasing priority order).

To be noticed : Operators must be written and spaces are allowed. No implicit multiplication is allowed.

Parenthesis may be used.

Function arguments must lay between braces.

The predefined functions are :

abs	absolute value.
sqrt	square root.
int	integer part.
sin	sine.
cos	cosine.
tan	tangent.
ln	neperian logarithm.
exp	exponential function.
asin	arcsine.
acos	arccosine.
atan	arctangent.
cosh	Hyperbolic cosine.
sinh	Hyperbolic sine.
tanh	Hyperbolic tangent.
asinh	Hyperbolic arcsine.
acosh	Hyperbolic arccosine.
atanh	Hyperbolic arctangent.
rand	returns a pseudo random double laying between 0 and 1 (0 included and 1 excluded).
²	square of a number.
fact(x)	returns x !. x must be integer, positive or null.
left(x)	If x is a calculation containing a test or an operation, returns the left member. Otherwise the calculation containing this formula will return the same calculation as x.
right(x)	If x is a calculation containing a test or an operation, returns the right. Otherwise the calculation containing this formula will return the same calculation as x.
core(x)	Returns the calculation equivalent to x where all calls to functions left, right and if are replaced by their effective argument and where all calls to user defined functions are replaced with the formula of the function.

The predefined functions of two variables are :

max(x, y)	returns the greater number of x and y.
min(x, y)	returns the lesser number of x and y.
pgcd(n, p)	returns the greater common divisor of n and p. n and p must be integer, positive and not null both.
ppcm(n, p)	returns the lesser common multiple of n and p. n and p must be integer positive.
mod(n, p)	returns the rest of euclidian division of n through b. n and p must be integer, positive and p not null .
ncr(n, p)	returns the number of subsets of p elements in a set of n elements. n and p must be integer, positive with p lower or equal to n.
npr(n, p)	returns the number of permutations of p elements in a set of n elements. n ans p must be integer, positive with p lower or equal to n.
divmaxp(n,p)	Returns the highest positive integer k such as n is divisible by k^p with 1 < p < 256 et 1 < \|n\| < 1000000

The predefined functions of three variables are :

if(cond, x, y)

returns x if cond equals 1 and y otherwise.

The predefined functions of four variables are :

integrale(expr, var, a, b)

returns an appoximated value of the integral of expr between a and b, var is the variable of integration.

The integral is calculated through Simpson's method with 400 intervals.

primitive(expr, var, start, a, b)

expr is a function of variable var. Returns f(b) - f(a).

The predefined functions of five variables are :

sum(expr, var, start, end, step)

returns sum of expression expr when all integer values in the range start-end with an increment of step are given to variable var.

expr may use all values or functions already defined.

start, end and step must have integer values.

prod(expr, var, start, end, step)

returns product of expression expr when all integer values in the range start-end with an increment of step are given to variable var .

expr may use all values or functions already defined.

start, end and step must have integer values.

Tests : They return a value which is 1 when result of the test is true, 0 otherwise.

a > b returns 1 if a is superior to b, 0 otherwise .

a < b returns 1 if a is inferior to b, 0 otherwise

a >= b returns 1 if a is superior to b or equal, 0 otherwise .

a <= b returns 1 if a is inferior to b or equal, 0 otherwise .

a = b returns 1 if a is equal to b, 0 otherwise .

a <> b returns 1 if a is different of b, 0 otherwise .

Boolean operators :

a&b : Returns 1 if a = 1 et b = 1 and 0 otherwise.

a|b : Returns 1 if a = 1 ou b = 1 et 0 otherwise.