Quick Guide
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| Function | Notation | Example |
|---|---|---|
| Exponent | ||
| square | x^2 | 10^2= 100 |
| cube | x^3 | 10^3= 1000 |
| power | x^n | 4^1.5= 8 |
| Root | ||
| square root | sqrt(x) | sqrt(25)= 5 |
| cube root | cbrt(x) | cbrt(27)= 3 |
| nth root | nrt(x, n) | nrt(32, 5)= 2 |
| Logarithm | ||
| general logarithm | log(x, n) | log(400, 20)= 2 |
| common logarithm | log(x) | log(10)= 1 |
| natural logarithm | ln(x) | ln(e)= 1 |
| Piecewise | ||
| absolute value | abs(x) | abs(-7)= 7 |
| floor | floor(x) | floor(3.8)= 3 |
| ceiling | ceil(x) | ceil(2.1) = 3 |
| round | round(x) | round(4.6) = 5 |
| modulo | x mod y | 12mod5= 2 |
| Trigonometry | ||
| sine | sin(x) | sin(π/2)= 1 |
| arcsine | asin(x) | asin(1)= 1.5707 |
| hyperbolic sine | sinh(x) | sinh(π/2)= 2.30129 |
| hyperbolic arcsine | asinh(x) | asinh(2.3)= 1.57027 |
| cosine | cos(x) | cos(0)= 1 |
| arccos | acos(x) | acos(1)= 0 |
| hyperbolic cosine | cosh(x) | cosh(0)= 1 |
| hyperbolic arccosine | acosh(x) | acosh(1)= 0 |
| tangent | tan(x) | tan(π/4)= 1 |
| arctangent | atan(x) | atan(1)= 0.78539 |
| hyperbolic tangent | tanh(x) | tanh(π/2)= 0.91715 |
| hyperbolic arctangent | atanh(x) | atanh(.9172)= 1.5711 |
| cosecant | csc(x) | csc(π/2)= 1 |
| arccosecant | acsc(x) | acsc(1)= 1.57079 |
| hyperbolic cosecant | csch(x) | csch(π/2)= 0.43454 |
| hyperbolic arccosecant | acsch(x) | acsch(.434)= 1.5719 |
| secant | sec(x) | sec(0)= 1 |
| arcsecant | asec(x) | asec(1)= 0 |
| hyperbolic secant | sech(x) | sech(0)= 1 |
| hyperbolic arcsecant | asech(x) | asech(1)= 0 |
| cotangent | cot(x) | cot(π/2)= 0 |
| arccotangent | acot(x) | acot(0)= 1.57079 |
| hyperbolic cotangent | coth(x) | coth(π)= 1.0037 |
| hyperbolic arccotangent | acoth(x) | acoth(1.003)= 3.1472 |
| Probability | ||
| combination | nCr(n, r) | nCr(20, 3)= 1140 |
| permutation | nPr(n, r) | nPr(20, 3)= 6840 |
| factorial | x! | 6!= 720 |
| Statistics | ||
| sum | sum(x, y, z, ...) | sum(1,2,3)= 6 |
| product | prod(x, y, z, ...) | prod(7,2,3)= 42 |
| min | min(x, y, z, ...) | min(8,2,9)= 2 |
| max | max(x, y, z, ...) | min(8,2,9)= 9 |
| median | median(x, y, z, ...) | median(8,2,9)= 8 |
| mean | mean(x, y, z, ...) | mean(2,9,4)= 5 |
| standard deviation | std(x, y, z, ...) | std(8,4,6)= 2 |
| variance | variance(x, y, z, ...) | variance(8,4,6)= 4 |
| Vector | ||
| dot product | x · y | [0,1]*[2,3]= 3 |
| cross product | cross(x, y) | cross([0,1,2],[3,4,5])= [-3,6,-3] |
| norm | norm(x) | norm([0,1,2])= 2.236068 |
| Matrix | ||
| determinant | det(x) | det([[1,2][3,4]])= -2 |
| inverse | inv(x) | inv([[1,2][3,4]])= [[-2,1],[1.5,-0.5]] |
| pseudoinverse | pinv(x) | pinv([[1,2][3,4]])= [[-2,1],[1.5,-0.5]] |
| trace | trace(x) | trace([[1,2][3,4]])= 5 |
| transpose | transpose(x) | transpose([[1,2][3,4]])= [[1,3],[2,4]] |
| Complex Numbers | ||
| argument | arg(x) | arg(3 + 2i)= 0.588002603548 |
| conjugate | conj(x) | conj(3 + 2i)= 3 - 2i |