A complex calculus is allowed to 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 complex functions are :
abs |
Module of a complex. Result is a complex number of imaginary part 0. |
conj |
Complex conjugate. |
angle |
Returns a complex number imaginary part of which is zero and real part of which is principal argument of the complex given as argument. |
re |
Returns a complex number imaginary part of which is zero and real part of which is the real part of the complex given as argument. |
im |
Returns a complex number imaginary part of which is zero and imaginary part of which is the real part of the complex given as argument. |
sqrt |
Square root. If the argument is not real or is strictly negative, the result doesn't exist. |
int |
Integer part. If the argument is not real, the result doesn't exist. |
sin |
complex sine. |
cos |
complex cosine. |
tan |
complex tangent. |
ln |
complex neperian logarithm. |
exp |
complex exponential. |
asin |
arcsine. If the argument is not real, the result doesn't exist. |
acos |
arcsine. If the argument is not real or doesn't lay between -1 and 1, the result doesn't exist. |
atan |
arctangent. If the argument is not real, the result doesn't exist. |
cosh |
Hyperbolic cosine |
sinh |
Hyperbolic sine |
tanh |
Hyperbolic tangent |
asinh |
Hyperbolic arcsine. If the argument is not real, the result doesn't exist. |
acosh |
Hyperbolic arccosine.If the argument is not real is strictly inferior to 1, the result doesn't exist.. |
atanh |
Hyperbolic arctangent. If the argument is not real or doesn't lay strictly between -1 and +1, the result doesn't exist. |
rand |
Returns a complex number containing a real value which is a pseudo-random real number lying between 0 and 1 (0 excluded and 1 included). |
² |
Square. |
fact(z) |
returns z !. z must be real, integer, positive or null. |
left(z) |
If z 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 z. |
right(z) |
If x is a calculation containing a test or an operation, returns the right member. Otherwise the calculation containing this formula will return the same calculation as x. |
The predefined complex functions of two variables are :
max(z, z') |
returns the greater number of z and z'. z and z' must be real. |
min(z, z') |
returns the lowest number of z and z'. z and z' must be real. |
pgcd(z, z') |
returns the GCD of z and z'. z and z' must be real, integer positive and not null. |
ppcm(z, z') |
returns the LCM of z and z'. z and z' must be real, integer positive and not null. |
mod(z, z') |
returns the rest of the integer division of z by z'. z and z' must be real and integer positive with b not null. |
ncr(z, z') |
returns the number of subsets of z' elements in a set of z elements. z and z' must be real, integer positive with z' lower or equal to z. |
npr(z, z') |
returns the number of permutations of z' elements in a set of z elements. z and z' must be real, integer positive with z' lower or equal to z. |
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 :
integral(expr, var, a, b) |
returns an appoximated value of the integral of expr between a and b, var is the variable of integration. a and b must be real. The integral is calculated through Simpson's method with 400 intervals. |
primitive(expr, var, 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. |
The tests: In complex calculus,the test exist only if the two arguments are real. They return a complex value which is 1 when the result is true, zero otherwise.
a > b return 1 if a > b and zero otherwise.
a < b return 1 if a < b and zero otherwise.
a >= b return 1 if a >= b and zero otherwise.
a <= b return 1 if a <= b and zero otherwise.
a = b return 1 if a = b and zero otherwise.
a <> b return 1 if a is not equal to b and zero 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.