Toolbox

At any time when editing a calculation or expression, you can press Toolbox. A catalogue of functions will open to help you make more specific calculations.

The Toolbox catalog is divided into several thematic sub-sections: Calculation, Complex numbers, Combinatorics, … Choose the calculation you want to perform and press OK. Complete the space between the parentheses with the arguments you need for each function.

The first three functions in the Toolbox catalogue are: Absolute value, n-th root and Logarithm to base a.

Function Description
abs(x) Calculates the absolute value of the argument you enter in parentheses. abs(-4.5) gives the value of 4.5\mid -4.5\mid, that is 4.54.5.
root(x,n) Calculates the nn-th root of a number. You must enter nn and xx in parentheses. root(x,n) gives the value of xn\sqrt[n\,]{x}. The value of nn may not be an integer.
log(x,a) Calculates the logarithm to base aa. You must enter aa and xx in parentheses. log(x,a) gives the value of loga(x)\log_{a}(x).

Calculation

Function Description
diff(f(x),a) Calculates the derivative of a function at a point. Be careful to define the function using the xx variable. diff(f(x),a) gives the value of f(a)f'(a). For example, to calculate the derivative of a square root at 5: diff(sqrt(x),5).
int(f(x),a,b) Calculates the integral of a function between two bounds. Be careful to define the function using the xx variable. int(f(x),a,b) gives the value of abf(x)dx\int_{a}^{b} f(x) \, \mathrm{d}x. For example, to calculate the integral of the square root between 00 and 55: int(sqrt(x),0,5).
sum(f(n),nmin,nmax) Calculates the sums of terms in nn. Be careful to define the terms with the variable nn. sum(f(n),nmin,nmax) gives the value of n=nminnmaxf(n)\sum_{n=n_{min}}^{n_{max}} f(n).
product(f(n),nmin,nmax) Calculates the products of terms in nn. Be careful to define the terms with the variable nn. product(f(n),nmin,nmax) gives the value of n=nminnmaxf(n)\prod_{n=n_{min}}^{n_{max}} f(n).

Complex numbers

Function Description
abs(x) Absolute value of a complex number. abs(2+3i)gives the value of 2+3i\mid 2+3i\mid.
arg(z) Argument of a complex number. arg(2+3i) gives the value of arg(2+3i)arg(2+3i) in radians.
re(z) Real part of a complex number. For instance, re(2+3i) returns 22.
im(z) Imaginary part of a complex number. For instance, im(2+3i) returns 33.
conj(z) Conjugate of a complex number. conj(2+3i) returns the conjugate of 2+3i2+3i, that 23i2-3i.

Combinatorics

Function Description
binomial(n,k) Number of ways to choose a subset of size kk elements, disregarding their order, from a set of nn elements. binomial(n,k) returns (nk)\dbinom{n}{k}, that is n!k!(nk)!\frac{n!}{k! (n-k)!}.
permute(n,k) Number of different ordered arrangements of a kk-element subset of an nn-set. permute(n,k) returns AnkA_{n}^k, that is n!(nk)!\frac{n!}{(n-k)!}.

Arithmetic

Function Description
gcd(p,q) Greatest Common Divisor of two integers. For instance, gcd(55,11) returns 1111.
lcm(p,q) Least Common Multiple of two integers. For instance, lcm(13,2) returns 2626.
factor(n) Integer factorization of nn. For instance, factor(24)returns 23×32^3 \times 3.
rem(p,q) Remainder of the Euclidian division of pp by qq. For instance, rem(50,45) returns the remainder of the division of 5050 by 4545 that is 55.
quo(p,q) Quotient of the Euclidian division of pp by qq. For instance, quo(80,39) returns the quotient of the division of 8080 by 3939 that is 22.

Matrix

Function Description
inverse(M) Inverse of the matrix M. For instance, inverse([[0.25,0][0,0.25]])returns [4004]\left[\begin{array}{cc}4 & 0 \\ 0 & 4 \end{array}\right].
det(M) Determinant of the matrix M. For instance, det([[1,2][3,4]]) returns 2-2.
transpose(M) Transpose of the matrix M. For instance, transpose([[1,2][3,4]]) returns [1324]\left[\begin{array}{cc}1 & 3 \\ 2 & 4 \end{array}\right].
trace(M) Trace of the matrix M. For instance, trace([[1,2][3,4]]) returns 55.
dim(M) Size of the matrix M. For instance, dim([[1,2][3,4]]) returns [2,2].

Random and approximation

Function Description
random() Generates a random number between 00 and 11.
randint(a,b) Generates a random integer aa and bb.
floor(x) Floor function. For instance, floor(5.8) returns 55.
frac(x) Fractional part. For instance, frac(5.8) returns 0.80.8.
ceil(x) Ceiling function. For instance, ceil(5.8) returns 66.
round(x,n) Rounds a number to nn digits after the decimal point. For instance round(8.6576,2) returns 8.668.66.

Hyperbolic trigonometry

Function Description
cosh(x) Hyperbolic cosine.
sinh(x) Hyperbolic sine.
tanh(x) Hyperbolic tangent.
acosh(x) Inverse hyperbolic cosine.
asinh(x) Inverse hyperbolic sine.
atanh(x) Inverse hyperbolic tangent.

Prediction interval

Function Description
prediction95(p,n) Prediction interval 95%. prediction95(p,n) returns [p1.96p(1p)n;p+1.96p(1p)n]\left[ p-1.96\frac{\sqrt{p(1-p)}}{\sqrt{n}};p+1.96\frac{\sqrt{p(1-p)}}{\sqrt{n}} \right].
prediction(p,n) Approximation of the prediction interval. prediction(p,n) returns [p1n;p+1n]\left[ p-\frac{1}{\sqrt{n}};p+\frac{1}{\sqrt{n}} \right].
confidence(f,n) 95% confidence interval. confidence(f,n) returns [f1n;f+1n]\left[ f-\frac{1}{\sqrt{n}};f+\frac{1}{\sqrt{n}} \right].