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Operations on Symbolic Expressions Guide

Task: get basic knowledge of how to work with Symbolic Toolbox in the MATLAB software package (Part 2).

Operations on Symbolic Expressions

Once an expression or variable is declared as a symbolic object, we can perform standard mathematical operations such as given in the table below.

Function Description Function Description
horner(S) transforms S into the Horner nested polynomial format
[N,D] = numden(S) returns two symbolic numerator and denominator expressions
sym(S,’?’); where ? may be f,r,e, or d symbolic to numeric conversion: f is floating point, r = rational form, e = rational plus an error term, d = decimal expansion when followed by digits(N)
poly2sym(c) converts the polynomial vector c into a symbolic polynomial
pretty(S) produces a typeset type display
A+B symbolic addition of A+B
A/B symbolic division of A/B
A*B symbolic multiplication of AB
S^p symbolic power S^p
A-B symbolic subtraction A-B

Example:

    \[ p_{1}=\frac{1}{y - 3} \]

    \[ p_{2}=\frac{3y}{y + 2} \]

    \[ p_{3}=(y + 4)(y - 3)y \]

syms y
p1 = 1/(y-3);
p2 = 3*y/(y+2);
p3 = (y+4) *(y-3) *y;

% Now operate:

    \[ p_{1}*p_{2}=\frac{1}{y - 3} * \frac{3y}{y + 2} \]

    \[ p_{1}*p_{3}=(y + 4)*y \]

    \[ p_{2}^{3}=\frac{27*y^{3}}{(y + 2)^{3}} \]

    \[ p_{1}+p_{2}=\frac{1}{y - 3} + \frac{3y}{y + 2} \]

    \[ [num,den] = numden(p_{1}+p_{2}) \]

    \[ num=-8*y+2+3*y^{2} \]

    \[ den = (y-3)*(y+2) \]

Solutions to Equations

To solve a single equation, we use:

g = solve(eq,var);

That is, find what value of the independent variable makes eq = 0; var is optional.

– If more than one variable is present, the variable to solve for set with var is:

S = sym('x^{2} + 3*x + 18');
solve(S)

    \[ x=[-\frac{3}{2}+\frac{3}{2}*i*7^{\frac{1}{2}}, -\frac{3}{2}-\frac{3}{2}*i*7^{\frac{1}{2}}] \]

syms \, x \, a \, b \, c

S = sym('a*x^2 + b*x + c'); % Contains four variables

solve(S,x) % Solve for x

    \[ x=[\frac{\frac{1}{2}}{a*(-b+(b^{2}-4*a*c)^\frac{1}{2}}), \frac{\frac{1}{2}}{a*(-b-(b^{2}-4*a*c)^\frac{1}{2}}] \]

%quadratic equation

To solve a system of equations, use:

g = solve(eq_{1},eq_{2},...,eq_{n},var_{1},var_{2},...,var_{n});

The var_{1}, …,var_{n}are the variables to solve for. They must be declared as symbolics using syms.

syms \, x \, y \, z
eq_{4} = sym('3*x+2*y-z=10');
eq_{5} = sym('-x+3*y+2*z=5');
eq_{6} = sym('x-y-z=-1');
solve(eq_{4},eq_{5},eq_{6},x,y,z);

x = -2

y = 5

z = -6


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The Example of Working with the Symbolic Toolbox in the MATLAB

Task: get basic knowledge of how to work with the symbolic toolbox in the MATLAB software package (Part 1).

Solution:

MATLAB is probably best known for its capability to perform numerical computations. This is particularly true when you consider the native capability of MATLAB itself. With the addition of the Symbolic Math Toolbox included in the student edition and the Extended Symbolic Math Toolbox, however, MATLAB can perform true symbol computations. MATLAB achieves its symbolic capability via the symbolic processor engine. Continue reading

A Guideon Pendulum Wave Effect in MapleSim

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Basics of Using InDesign: Part III

In the text below we continue talking about the basics of using InDesign. We remind you that the article is designed for students and beginners who are familiar with the basics of Adobe Photoshop, have initial skills in Adobe Illustrator or CorelDraw, and want to learn how to create multi-page text documents. In the following article you will learn how to embed files into InDesign.

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Guide on How to Use InDesign: Part II

In this article we continue describing the basic information on how to use InDesign. With the help of Indesign you will be able to create amazing design templates, interactive documents in PDF format, and even impressive videos for Adobe Flash Player. With our guide you will learn how to use InDesign standard functions. This text is aimed at students and beginners that only have just started using the software and need basic information. Also, we consider that you already know how to work with graphic editors and modular grids. For more information we advise you to check the first part of this tutorial on our blog.

We hope that our guide will help you a lot! In addition, on our blog we frequently post solutions for assignments and guides on various subjects. You may find it helpful, especially when you are assigned a similar task. All materials are supported with screenshots, images, and detailed descriptions to help you get a better understanding of the subject. Continue reading

Guide on How to Use Adobe InDesign: Part I

InDesign, in our opinion, is one of the easiest and most convenient programs for creating multi-page editions. While it has a wide range of functions, it is very easy to learn how to use Adobe InDesign. Besides, the compatibility with other programs of the Adobe System makes it simply priceless for every designer. What can you do with InDesign? Usually it is used for creating booklets, catalogs, books, newspapers, magazines, etc. If you have a strong desire to learn how to use Adobe InDesign, this article should help you.

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Step-by-Step Guide: Hello World Java NetBeans

If you have decided to learn Java NetBeans, start with learning the simple application Hello World. If you will open any book about programming language you will see that the first application every programmer creates is Hello World. This application demonstrates the basic methods and serves as a great beginning for you. In the following article you can read a step-by-step tutorial on how to create Hello World Java NetBeans.

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Multisim Circuit Examples: DC Sweep and Transient Analysis

If you are attending engineering classes, you will probably face an assignment that will ask you to create a simulation of a certain circuit in Multisim. While Multisim has an intuitive and simple interface, technologies used to create high-quality simulations are quite difficult. In the following Multisim circuit examples you will learn how to construct a particular circuit using DC sweep and transient analysis.

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