# Constructing and working with Polynomials in the PSLab Android App

PSLab is a device that allows the user to perform a range of science and engineering experiments. PSLab has existing communication library (PSLab Desktop) written in Python. Since we are developing an Android application to operate PSLab, the initial step was to port Python code to JAVA. In PSLab Android application we are using version 3.6.1 of Apache Maths Commons.

NumPy is the package for scientific computing with Python. Polynomials in NumPy can be created using numpy.poly1d. Since some of the files in PSLab Desktop use polynomials, it was important to find a package in JAVA that provides features equivalent to NumPy. Apache Maths Commons fulfilled our needs. It is a Mathematics Library available in JAVA, that provides the means to construct polynomials and perform a range of operations on them. A detailed documentation of the library is available here.

import numpy

p = numpy.poly1d([1, 2, 3])

print(numpy.poly1d(p))

q = p(0.5)

print q

Output:

1 x2 + 2 x + 3

4.25

Poly1d() function converts a list into polynomials. The first element of the list is the coefficient of the highest degree of the polynomial while the last element is the coefficient of lowest degree of the polynomial. While p(0.5) evaluates polynomial at x = 0.5.

Now let’s construct polynomials in JAVA using Apache Maths Commons

public class poly {

public static void main(String[] args){

PolynomialFunction p = new PolynomialFunction(new double[]{3, 2, 1});

System.out.println(p);

System.out.println(p.value(0.5));

}
}

Output:

3 + 2 x + x^2

4.25

Polynomial Function converts the double array into polynomials. The first element of the array is the coefficient of the lowest degree of the polynomial while the last element is the coefficient of the highest degree of the polynomial. p.value (0.5) evaluates polynomial at x = 0.5.

Other things we can do

• ###### Find the degree of the polynomial.

Continuing with the above example where polynomial was 3 + 2 x + x^2. p.degree() gives 2 as output which is the degree of the given polynomial.

• ###### Get the coefficients of the polynomial

p.getCoefficients() returns a double array of the coefficients of the given polynomial. In the above case [3.0, 2.0, 1.0] will be returned.

• ###### Find derivatives of the polynomial

p.derivative() returns 2 + 2 x which is derivative of polynomial 3 + 2 x + x^2.

• ###### Add, subtract and multiply two polynomials.

We can add, subtract and multiply 2 polynomials. For example p.multiply(new  Polynomial Function(new double[]{1,2})) returns 3 + 8 x + 5 x^2 + 2 x^3 which is  the product of 3 + 2 x + x^2 and 1 + 2 x

#### Where are they are used in PSLab?

Polynomials are used in AnalogInputSource.java  to convert raw ADC codes (0=0V , 1023=3.3V ) to voltage values.

• calPoly10 = new PolynomialFunction(new double[]{0., 3.3 / 1023, 0.});
• calPoly12 = new PolynomialFunction(new double[]{0., 3.3 / 4095, 0.});

Polynomials are also used in DACChannel.java to convert DAC codes to voltage values and vice versa.

• VToCode = new PolynomialFunction(new double[]{-4095. * intercept / slope, 4095. / slope});
• CodeToV = new PolynomialFunction(new double[]{intercept, slope / 4095.});

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