# 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:

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

% Now operate:

Solutions to Equations

To solve a single equation, we use:

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

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

% Contains four variables

% Solve for

To solve a system of equations, use:

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

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