See Also: Calculator Nonlinear
Equations Solver Differential Equations Solver
See Also: Calculator Nonlinear
Equations Solver Differential Equations Solver
The following objects compose a valid Polymath math expression:
| Expression Objects | Description | Examples |
| Number | A number can be represented in decimal
notation or engineering notation. Engineering notation can be used to
indicate powers of 10 using 'e' or 'E' for example, 0.123e-5 is the same as
0.123*10^(-5). Note that only the period "." is used as the decimal delimiter symbol and comma nor spaces must not be used to indicate digits grouping. |
1.0, 2300, 5E-7, 1.23E+9, 34.0046 Invalid Polymath numbers: 5,000.00 12,9 12 000 000 |
| Variable name | Variable names must begin with an alphabetical character and can contain alphabetic and numeric characters or underscore “_”. Variable names are case-sensitive, i.e. 't' and 'T' are two different variables. Special characters such as $, &, #, @ etc. are not allowed. | x1, x2, A12, T, tm4eee, VH2O, PmmHg, KL_1 |
| Arithmetic operator | Returns the arithmetic operations of the binary
components. For example '2+3' returns 5 The '^' symbol is used for exponentiation. The +, -, *, / symbols are used for addition, subtraction, multiplication, and division respectively. The precedence of operators is ^, (* or /), (+ or -) which is invoked working from left to right in an expression. |
+, -, *, /, ^
(1 + 2 * 3 ^ 2 ^ 3 / 2 - 4) is equivalent to (1 + (2 * (((3 ^ 2) ^ 3) / 2)) - 4) |
| Function name | Various mathematical function names are
available. Examples: sin, cos, exp, ... The full list of available Polymath functions is presented below. |
12+sin(4) exp( 5*9+log(8)) |
| Condition operator |
These operators return "1" if the
condition met, and "0" if the condition does not meet. |
>, <, >=, <=, == |
| Boolean operator |
The Boolean operators return "1"
if the condition is met, and "0" if the condition is not met. |
And, Or |
| If-Then-Else | There are three case-insensitive keywords which compose the
if-then-else expression structure. The three keywords are: If, Then, Else. |
If (2>5) Then (sin(12)+4) Else (sin(12)+8) if(2>5)then(sin(12)+4)else(sin(12)+8) |
| Parenthesis | Open Parenthesis: ( Close Parenthesis: ) |
x+(3-2) |
A special 'if' statement is available, with the following syntax:
if (condition) then (expression1) else (expression2)
The parentheses are optional.
The condition may include the following operators: and, or (Boolean operators), >
(greater than),
< (less than), >= (greater than or equal), <= (less than or equal), == (equals).
The expressions may be any formula, including another 'if' statement.
- For example:
A = if (x>0) then (log(x)) else(0)
b = if (T<minT) then (minT) else (if (T>maxT) then (maxT) else (T))
Vol_h1 = if (a>5 and c<2) then 1.12 else 7.89
| Function Name | Description |
| abs ( ) | absolute value |
| arccos ( ) | trigonometric inverse cosine with result in radians |
| arccosec ( ) | trigonometric inverse cosecant with result in radians |
| arccosech ( ) | inverse hyperbolic cosecant |
| arcsech () | inverse hyperbolic secant |
| arccosh ( ) | inverse hyperbolic cosine |
| arccotan ( ) | trigonometric inverse cotangent with result in radians |
| arccotanh ( ) | inverse hyperbolic cotangent |
| arcsec ( ) | trigonometric inverse secant with result in radians |
| arcsin ( ) | trigonometric inverse sine with result in radians |
| arcsinh ( ) | inverse hyperbolic sine |
| arctan ( ) | trigonometric inverse tangent with result in radians |
| arctanh ( ) | inverse hyperbolic tangent |
| cbrt ( ) | cubic root |
| cos ( ) | trigonometric cosine with argument in radians |
| cosec ( ) | trigonometric cosecant with argument in radians |
| cosech ( ) | hyperbolic cosecant |
| cosh ( ) | hyperbolic cosine |
| cotan ( ) | trigonometric cotangent with argument in radians |
| coth ( ) | hyperbolic cotangent |
| exp ( ) | exponential (e^x ) |
| erf ( ) | error function |
| exp10 ( ) | exponential of 10 (10^x ) |
| exp2 ( ) | exponential of 2 (2^x ) |
| fact ( N ) | factorial of integer part of number N (this only operates on a number) |
| frac ( ) | fractional part |
| int ( ) | integer part |
| ln ( ) | natural logarithm to the base e |
| log ( ) | logarithm to the base 10 |
| psi ( ) | psi function |
| rand ( ) |
Returns a random number between 0-1. |
| round ( ) | rounded value |
| sec ( ) | trigonometric secant with argument in radians |
| sech ( ) | hyperbolic secant |
| sign ( ) | returns + 1 or 0 or -1 |
| sin ( ) | trigonometric sine with argument in radians |
| sinh ( ) | hyperbolic sine |
| sqrt ( ) | square root |
| tan ( ) | trigonometric tangent with argument in radians |
| tanh ( ) | hyperbolic tangent |
All function names must be given in lower-case letters. The trigonometric functions require that their arguments be given in radians. Conversely, the inverse trigonometric functions give their results in radians.
You should note that the functions require that their arguments be enclosed in parentheses, but that the arguments do not have to be simple numbers. You may have a complicated expression as the argument for a function, and you may even nest the functions, using one function (or an expression including one or more functions) as the argument for another.