Version 2.3: This web tool evaluates any real and complex expression.
It supports the usual arithmetic operators, build-in constants and built-in functions.
Arithmetic Operators:
+,-,*,/ ,% and ^
Example:
2+3*5-1 which evaluates to 16. Or with complex numbers (2-i)*(5+i3) which evaluates to (13+i1), you can also do the power operator ^ with a complex number.
E.g. (2-i1)^(5+i3) which evaluates to approx. 223.6+i21.5
Relational Operators
>,<,>=,<=,== and !=
Example:
1>2 return false (same as 0). x==3 return true (same as 1) if the value of the variable is 3 otherwise false
Boolean operators
? &,|,&&,||
Example:
x>y||y==3 returns true is x>y or y==3.
Build in constants:
Constants | Math Symbol | Value |
PI | Π | 3.141592653589793 |
E | E | 2.718281828459045 |
LN10 | Loge10 | 2.302585092994046 |
LN2 | Loge2 | 0.6931471805599453 |
LOG10E | Log10e | 0.4342944819032518 |
LOG2E | Log102 | 1.4426950408889633 |
INFINITY | +∞ | +∞ |
SQRT2 | √2 | 1.4142135623730951 |
SQRT1_2 | 1/√2 | 0.7071067811865476 |
Build-in constant can't be overwritten by the assignment statement. E.g. LN2=10 will return a syntax error message.
Implicit multiplication is also supported e.g. 2PI evaluates to approx. 6.28 and 5(sqrt(2)+2) evaluates to approx. 17.07
Assignment Statement: You can use the assignment statement (= assignment operator) to save the result in a variable.
E.g. x=2 and then later use the variable x in a later statement or expression e.g. sqrt(x).
You can change the contents of the variable with a new assignment statement.
Build-in functions:
abs, acos, asin, atan, atan2*, asinh, acosh, atanh, ceil*, cosh, cos, exp, floor*, gcd*, norm, imag, ipow lcm*,log, max*, min*, pow,
random**, real, round*, sinh, sin, sqrt, tanh, tan.
**) marked are functions that take zero arguments. *) marked are functions that only take real arguments,
all other takes real or complex arguments. e.g. sqrt(2-i2) evaluates to approx. (1.55+i0.64).
Build-in functions can't be overwritten by the assignment statement. E.g. sin=3 will give a syntax error message.
Two new basic built-in functions have been added. gcd(a,b,c,...) which finds the greatest common divisor of the numbers. E.g. gcd(4,7,8) return 1.
lcm(a,b,c,...) find the least common multiplier e.g. lcm(4,7,8) return 56.
min() and max() have been expanded to also accept vector or matrix as arguments.
Variables: You can also assign an expression to a variable for later use: e.g. x=sqrt(2-i2)*3/4 and then used them later.
E.g. y=log(123.5)/x etc.
Functions: In version 1.2 we have added functions. First, you would need to define a function as in the following:
f(x)=2*sqrt(x)
and then just call the function with a parameter e.g.:
3*log(f(4))
Compound Statements: You can use compound statements in functions or just in general to create a block of statements. e.g.
f(x)={ y=x; y=3+y; z=5; }
Comma Expressions:? Can also be useful when you want to evaluate several expressions in a function but only return the last expression
as the result of the function call. E.g.
f(x)={ y=2, x=sqrt(x)/y, log(x+2) }
here log(x+2) is returned as the value of the function to be used in another statement.
In a function call, you can have as many parameters as you like however, the number of parameters passed to a function must match the definition of the functions.
Example: Durand-Kerner method on a polynomial f(x)=x^3-3*x^2+3*x-5
Add each line below to the input field and hit the evaluate button after each line. Then type in next() and see the value of the roots for each iteration.
p=(0.4 + 0.9 i)^0, q=(0.4 + 0.9 i)^1, r=(0.4 + 0.9 i)^2
f(x)=x^3-3*x^2+3*x-5
next()={dp=f(p)/((p-q)*(p-r)); p=p-dp; dq=f(q)/((q-p)*(q-r));q=q-dq;dr=f(r)/((r-p)*(r-q));r=r-dr;}
Conditional expression was added in version 1.10. This is the same as the ? operator in the c language. E.g. x = y>10 ? y : y*2;
Vectors and Matrix: Were added in version 2.0. A Vector can be created as a row vector:
v=[1,2,3] or as column vectors as v=[[1],[2],[3]] and a vectors element can be accessed simply by v[1] which selects
the number 2 from the vector v. A vector first index 0.
A matrix can be defined using similar notation e.g.
m=[[1,2],[3,4]] which is a 2 by 2 matrix or a 3x2 matrix as in m=[[1,2,3],[4,5,6]]
you can used vector and matrix with the +,-,* and / operator. A matrix element can be accessed using row and column index as in m[1,2]
whichs select the element 6. Matrix indexes like Vectors always start with index 0. m[0,0] select the first element 1.
A vector or matrix element can also be complex numbers e.g.
v=[1-i,1+i,3]
A few matrix functions have been added. transpose(m) transpose a vector or matrix elements. determinant(m) returns the determinant of the matrix and finally,
a new function solveAxb(a,b) has been added. It solved the set of linear equations expressed by Ax=b. c can be a vector or a matrix.
Build-in Vector/Matrix function with the support of vector and matrix in version 2 there is also a specific build-in function supporting
vector/matrix operation.
Diagonal, determinant, norm, solveAxb, transpose
Final Note: If you refresh your browser or exit you lose all variables.
The History section keeps track of your previous expression evaluations. Email me if you encounter any problems at hve@hvks.com
Build in function/method
Math Functions.
Notice that x or y as an argument indicates only a real argument.
z indicates a complex argument.
... indicates a variable number of arguments
Method | Description |
abs(z,...) | Returns the absolute value of z |
acos(z) | Returns the arccosine of z, in radians |
acosh(z) | Returns the arccosine hyperbolic of z |
asin(z) | Returns the arcsine of z, in radians |
asinh(z) | Returns the arcsine hyperbolic of z |
atan(z) | Returns the arctangent of z as a numeric value between -PI/2 and PI/2 radians |
atanh(z) | Returns the arctangent hyperbolic of z |
atan2(y, x) | Returns the arctangent of the quotient of its arguments |
ceil(x) | Returns the value of x rounded up to its nearest integer |
cos(z) | Returns the cosine of z (z is in radians) |
cosh(z) | Returns the cosine hyperbolic of z |
exp(z) | Returns the value of Ez |
floor(x) | Returns the value of x rounded down to its nearest integer |
gcd(x,y,...,n) | Returns the greatest common divisor of the numbers |
imag(z) | Returns the imaginary part of a complex number |
ipow(z,y) | Return the zy, where y is an integer |
lcm(x,y,...,n) | Returns the least common multiplier of the numbers |
log(z) | Returns the natural logarithm (base E) of z |
max(x,y,...,n) | Returns the number with the highest value |
min(x,y,...,n) | Returns the number with the lowest value |
pow(z, y) | Returns the value of z to the power of y. Notice y can be a complex number as well |
random() | Returns a random number between 0 and 1 |
real(z) | Return the real part of a complex number z |
round(x) | Returns the value of x rounded to its nearest integer |
sin(z) | Returns the sine of z (z is in radians) |
sinh(z) | Returns the sine hyperbolic of z |
sqrt(z) | Returns the square root of z |
tan(z) | Returns the tangent of z |
tanh(z) | Returns the tangent hyperbolic of z |
Vector/Matrix functions
Method | Description |
diagonal(v) | Create and return a diagonal matrix with the diagonal value of vector v |
determinant(m) | Returns the determinant of the square matrix m |
norm(v,[p-norm]) | Returns the norm given by p-norm of the vector v. if p-norm is omitted p-norm defaults to 2 |
solveAxb(A,b) | Solve the matrix equation Ax=b where A is a square matrix and b is a column vector or a matrix. If b is a column vector
x is also a column vector, if b is a matrix then x is returned as a matrix for the solution |
transpose(v) | Transpose of the vector or matrix. E.g. a row vector becomes a column vector |
Notice there is no direct function for matrix inversion. However, if m is a square matrix then the expression 1/m calculates the inverse matrix.
