Real calculus syntax

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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.

log

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 excluded and 1 included).

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.


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.


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.


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.

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