Otter - Numeric Calculus

This python package is made for applied Numeric Calculus of Algebra Functions. It is made with the following objectives in mind:

• Receive one variable function from user input

• Receive two variable function from user input

• Performe derivatives with one variable functions

• Performe integral with received functions

• Find root of functions throw method of bissection and method of newton

• Solve Diferential Equations throw method of euler and runge

• Performe Minimus Interpolation and Polinomial Interpolation

Syntax

To initialize a Otter instance linked to functions use the following syntax otr = Otter.algebra(f), where otr will be a arbitrary name for the instance and f is a function of one variable.

To initialize a Otter instance linked to data and interpolation use the following syntax otr = Otter.interpolation(data), where otr will be a arbitrary name for the instance and data will be a numpy matrix where the first columns has to contain the values for x and the second column contains the values for y.

Algebra

Algebra is a Python Class where some of the features described previously are defined as Classes as well, like: Integral, Roots, EDO (diferential equations).

Integral

To call the class Integral append the sufix with lower case in front of the instance like: otr.integral. The Integral class has two other class defined inside, Simple and Double, to call them append the sufix with lower case in front as otr.integral.simple or otr.integral.double. Then pick between Riemann's Method or Simpson's Method by appending the sufix riemann or simpson as well.

After that the syntax will be something like otr.integral.double.riemann(a,b,c,d,n,m), where a and c will be the first value of the interval of integration respectively in x and y, b and d will be the last, n and m will be the number of partitions.

The syntax for one variable integrations will be otr.integral.simple.riemann(a,b,n).

If n is not defined the standart value in 10^6 partitions for one variable and 10^4 for double. And if m is not defined the standart value will be equal to n.

Roots

To call the class Root append the sufix with lower case in front of the instance like: otr.roots. The Roots class has three methods defined inside, bissec, newton and bissec_newton, to call them append the sufix with lower case in front as otr.roots.bissec or otr.roots.newton or even otr.roots.bissecnewton.

The syntax for the bissection method and bissec_newton is equal to otr.roots.bissec(a,b,e) and otr.roots.bissec_newton(a,b,e), where a is the first element of the interval containing the root and b is the last, e being the precision.

The syntax for the newton method is equal to otr.roots.newton(a,e), where a is the element closest to the root and e is the precision.

If e is not defined the standart value is 10^(-6).

Diferential Equations

To call the class EDO (Equações Diferenciais Ordinárias) append the sufix with lower case in front of the instance like: otr.edo. The EDO class has two methods defined inside: euler and runge, to call them append the sufix with lower case in front as otr.edo.euler or otr.edo.runge.

The syntax for the diferential equations method is equal to otr.edo.euler(a,y,b,n) or otr.edo.runge(a,y,b,n), where a and y will be the inintial point and b is the value in x which you want to know the corresponding value in y and n is the number of operations.

If n is not defined the standart value is 10^7.

Interpolation

The python class Interpolation is divided in one method, minimus interpolation, and one class, polinomial interpolation.

To call the method minimus use a syntax like otr = Otter.interpolation(data), where data is a data frame containing values for x and y, otr is an instance and append the method in front of the instance like: otr.minimus(x), where x is value of f(x) you want to estimate.

To call the class Polinomial append the sufix with lower case in front of the instance like: otr.polinomial. The Polinomial class has four methods defined inside: vandermonde, lagrange, newton and gregory, to call them append the sufix with lower case in front like otr.edo.gregory(x) where x is value of f(x) you want to estimate.

Installation

To install the package from source cd into the directory and run:

pip install .

or run

pip install yoshi-otter