sympref

Set symbolic settings

Syntax

oldVal = sympref(pref,value)

oldVal = sympref(pref)

oldPrefs = sympref(prefs)

oldPrefs = sympref()

Description

oldVal = sympref(pref,value) sets the symbolic setting pref to value and returns the previous value of the setting to oldVal. You can set the setting to its default value using sympref(pref,'default').

Symbolic settings can affect the computation of the symbolic functions fourier, ifourier, and heaviside, and the display format of symbolic output.

oldVal = sympref(pref) returns the current value of pref.

oldPrefs = sympref(prefs) sets multiple symbolic settings to the values in the structure prefs and returns the previous values of all settings to oldPrefs. You can set all symbolic settings to their default values using sympref('default').

oldPrefs = sympref() returns the current values of all symbolic settings.

Note

Symbolic settings persist through successive MATLAB^® sessions. Opening a new session does not restore the default settings.

Examples

Change Parameter Values of Fourier Transform

The Fourier transform $\mathit{F}\left(\mathit{w}\right)$ of $\mathit{f}=\mathit{f}\left(\mathit{t}\right)$ is

$$\mathit{F}\left(\mathit{w}\right)=\mathit{c}{\int }_{-\infty }^{\infty }\mathit{f}\left(\mathit{t}\right){\mathit{e}}^{\mathit{i}\mathit{swt}}\mathit{dt},$$

where $\mathit{c}$ and $\mathit{s}$ are parameters with the default values 1 and –1, respectively. Other common values for $\mathit{c}$ are $1/\left(2\pi \right)$ and $1/\sqrt{2\pi }$, and other common values for $\mathit{s}$ are $1$, $-2\pi$, and $2\pi$.

Find the Fourier transform of sin(t) with default c and s parameters.

syms t w
F = fourier(sin(t),t,w)

F = $$-\pi \hspace{0.17em}\left(\delta \text{<a href="matlab:doc symbolic/dirac">dirac</a>}\left(w-1\right)-\delta \text{<a href="matlab:doc symbolic/dirac">dirac</a>}\left(w+1\right)\right)\hspace{0.17em}\mathrm{i}$$

Find the same Fourier transform with $\mathit{c}=1/\left(2\pi \right)$ and $\mathit{s}=1$. Set these parameter values by changing the 'FourierParameters' setting. Represent $\pi$ exactly by using sym. Specify the values of c and s as the vector [1/(2*sym(pi)) 1]. Store the previous values returned by sympref so that you can restore them later.

oldVal = sympref('FourierParameters',[1/(2*sym(pi)) 1])

oldVal = $$\left(\begin{array}{cc}1& -1\end{array}\right)$$

F = fourier(sin(t),t,w)

F = 
$$\frac{\delta \text{<a href="matlab:doc symbolic/dirac">dirac</a>}\left(w-1\right)\hspace{0.17em}\mathrm{i}}{2}-\frac{\delta \text{<a href="matlab:doc symbolic/dirac">dirac</a>}\left(w+1\right)\hspace{0.17em}\mathrm{i}}{2}$$

The settings that you set using sympref persist through your current and future MATLAB® sessions. Restore the previous values of c and s to oldVal.

sympref('FourierParameters',oldVal);

Alternatively, you can restore the default values of c and s by specifying the 'default' option.

sympref('FourierParameters','default');

Change Value of Heaviside Function at Origin

In Symbolic Math Toolbox™, the default value of the Heaviside function at the origin is 1/2. Return the value of heaviside(0). Find the Z-transform of heaviside(x) for this default value of heaviside(0).

syms x
H = heaviside(sym(0))

H = 
$$\frac{1}{2}$$

Z = ztrans(heaviside(x))

Z = 
$$\frac{1}{z-1}+\frac{1}{2}$$

Other common values for the Heaviside function at the origin are 0 and 1. Set heaviside(0) to 1 by changing the 'HeavisideAtOrigin' setting. Store the previous value returned by sympref so that you can restore it later.

oldVal = sympref('HeavisideAtOrigin',1)

oldVal = 
$$\frac{1}{2}$$

Check if the new value of heaviside(0) is 1. Find the Z-transform of heaviside(x) for this value.

H = heaviside(sym(0))

H = $$1$$

Z = ztrans(heaviside(x))

Z = 
$$\frac{1}{z-1}+1$$

The new output of heaviside(0) modifies the output of ztrans.

The settings that you set using sympref persist through your current and future MATLAB® sessions. Restore the previous value of heaviside(0) to oldVal.

sympref('HeavisideAtOrigin',oldVal);

Alternatively, you can restore the default value of 'HeavisideAtOrigin' by specifying the 'default' option.

sympref('HeavisideAtOrigin','default');

Modify Display of Symbolic Expressions in Live Scripts

By default, symbolic expressions in live scripts are displayed in abbreviated output format, and typeset in mathematical notation. You can turn off abbreviated output format and typesetting using symbolic settings.

Create a symbolic expression and return the output, which is abbreviated by default.

syms a b c d x 
f = a*x^3 + b*x^2 + c*x + d;
outputAbbrev = sin(f) + cos(f) + tan(f) + log(f) + 1/f

outputAbbrev = 
$$\begin{array}{l}\cos \left({\sigma }_1\right)+\log \left({\sigma }_1\right)+\sin \left({\sigma }_1\right)+\tan \left({\sigma }_1\right)+\frac{1}{{\sigma }_1}\\ \\ \mathrm{where}\\ \\ \mathrm{ }{\sigma }_1=a\hspace{0.17em}{x}^3+b\hspace{0.17em}{x}^2+c\hspace{0.17em}x+d\end{array}$$

Turn off abbreviated output format by setting 'AbbreviateOutput' to false. Redisplay the expression.

sympref('AbbreviateOutput',false);
outputLong = sin(f) + cos(f) + tan(f) + log(f) + 1/f

outputLong = 
$$\cos \left(a\hspace{0.17em}{x}^3+b\hspace{0.17em}{x}^2+c\hspace{0.17em}x+d\right)+\log \left(a\hspace{0.17em}{x}^3+b\hspace{0.17em}{x}^2+c\hspace{0.17em}x+d\right)+\sin \left(a\hspace{0.17em}{x}^3+b\hspace{0.17em}{x}^2+c\hspace{0.17em}x+d\right)+\tan \left(a\hspace{0.17em}{x}^3+b\hspace{0.17em}{x}^2+c\hspace{0.17em}x+d\right)+\frac{1}{a\hspace{0.17em}{x}^3+b\hspace{0.17em}{x}^2+c\hspace{0.17em}x+d}$$

Create another symbolic expression and return the output, which is typeset in mathematical notation by default. Turn off rendered output and use ASCII output instead by setting 'TypesetOutput' to false. First, show the typeset output.

syms a b c d x 
f = exp(a^b)+pi

f = $$\pi +{\mathrm{e}}^{a^b}$$

Turn off typesetting by setting 'TypesetOutput' to false. Redisplay the expression.

sympref('TypesetOutput',false);
f = exp(a^b)+pi

 
f =
 
pi + exp(a^b)
 

The settings that you set using sympref persist through your current and future MATLAB® sessions. Restore the default values of 'AbbreviateOutput' and 'TypesetOutput' by specifying the 'default' option.

sympref('AbbreviateOutput','default');
sympref('TypesetOutput','default');

Display Symbolic Results in Floating-Point Format

Display symbolic results in floating-point output format, that is the short, fixed-decimal format with 4 digits after the decimal point.

Create a quadratic equation.

syms x
eq = x^2 - 2e3/sym(pi)*x + 0.5 == 0

eq = 
$$x^2-\frac{2000\hspace{0.17em}x}{\pi }+\frac{1}{2}=0$$

Find the solutions of the equation using solve.

sols = solve(eq,x)

sols = 
$$\left(\begin{array}{c}-\frac{\sqrt{2}\hspace{0.17em}\sqrt{2000000-{\pi }^2}-2000}{2\hspace{0.17em}\pi }\\ \frac{\sqrt{2}\hspace{0.17em}\sqrt{2000000-{\pi }^2}+2000}{2\hspace{0.17em}\pi }\end{array}\right)$$

Set the 'FloatingPointOutput' setting to true. Display the quadratic equation and its solutions in floating-point format.

sympref('FloatingPointOutput',true);
eq

eq = $$x^2-636.6198\hspace{0.17em}x+0.5000=0$$

sols

sols = 
$$\left(\begin{array}{c}7.8540e-04\\ 636.6190\end{array}\right)$$

The floating-point format displays each symbolic number in the short, fixed-decimal format with 4 digits after the decimal point. The 'FloatingPointOutput' setting does not affect the floating-point precision in a symbolic computation. To compute symbolic numbers using floating-point arithmetic, use the vpa function.

Now restore the default value of 'FloatingPointOutput' by specifying the 'default' option. Compute the floating-point approximation of the solutions in 8 significant digits using vpa.

sympref('FloatingPointOutput','default');
sols = vpa(sols,8)

sols = 
$$\left(\begin{array}{c}0.00078539913\\ 636.61899\end{array}\right)$$

Modify Output Order of Symbolic Polynomial

Create a symbolic polynomial expression consisting of multiple variables. Display the polynomial in the default order.

syms x y a b
p1 = b^2*x^2 + a^2*x + y^3 + 2

p1 = $$a^2\hspace{0.17em}x+b^2\hspace{0.17em}{x}^2+y^3+2$$

The default option sorts the output in alphabetical order, without distinguishing the different symbolic variables in each monomial term.

Now display the same polynomial in ascending order by setting 'PolynomialDisplayStyle' to 'ascend'.

sympref('PolynomialDisplayStyle','ascend');
p1

p1 = $$2+y^3+a^2\hspace{0.17em}x+b^2\hspace{0.17em}{x}^2$$

The 'ascend' option sorts the output in ascending order based on the importance of the variables. Here, the most important variable x with the highest order in a monomial term is displayed last.

Display the polynomial in descending order by setting 'PolynomialDisplayStyle' to 'descend'.

sympref('PolynomialDisplayStyle','descend');
p1

p1 = $$b^2\hspace{0.17em}{x}^2+a^2\hspace{0.17em}x+y^3+2$$

The settings that you set using sympref persist through your current and future MATLAB® sessions. Restore the default value of 'PolynomialDisplayStyle' by specifying the 'default' option.

sympref('PolynomialDisplayStyle','default');

Modify Display of Symbolic Matrix in Live Scripts

By default, a symbolic matrix in live scripts is set in parentheses (round brackets). You can specify the use of square brackets instead by using sympref.

Create a symbolic matrix consisting of symbolic variables and numbers.

syms x y
A = [x*y, 2; 4, y^2]

A = 
$$\left(\begin{array}{cc}x\hspace{0.17em}y& 2\\ 4& y^2\end{array}\right)$$

Display the matrix with square brackets by setting 'MatrixWithSquareBrackets' to true.

sympref('MatrixWithSquareBrackets',true);
A

A = 
$$\left[\begin{array}{cc}x\hspace{0.17em}y& 2\\ 4& y^2\end{array}\right]$$

The settings that you set using sympref persist through your current and future MATLAB® sessions. Restore the default value by specifying the 'default' option.

sympref('MatrixWithSquareBrackets','default');

Save and Restore All Symbolic Settings

Instead of saving and restoring individual settings one by one, you can use sympref to save and restore all symbolic settings simultaneously.

Return a structure containing the values of all symbolic settings by using sympref().

oldPrefs = sympref()

oldPrefs = struct with fields:
           FourierParameters: [1    -1]
           HeavisideAtOrigin: 1/2
            AbbreviateOutput: 1
               TypesetOutput: 1
         FloatingPointOutput: 0
      PolynomialDisplayStyle: 'default'
    MatrixWithSquareBrackets: 0

Access the value of each symbolic setting by addressing the field of the structure. Alternatively, you can use the command sympref(pref).

val1 = oldPrefs.FourierParameters

val1 = $$\left(\begin{array}{cc}1& -1\end{array}\right)$$

val2 = oldPrefs.HeavisideAtOrigin

val2 = 
$$\frac{1}{2}$$

val3 = sympref('FourierParameters')

val3 = $$\left(\begin{array}{cc}1& -1\end{array}\right)$$

To modify multiple symbolic settings simultaneously, you can create a structure prefs that contains the setting values. Use the command sympref(prefs) to set multiple settings.

prefs.FourierParameters = [1/(2*sym(pi)) 1]

prefs = struct with fields:
    FourierParameters: [1/(2*pi)    1]

prefs.HeavisideAtOrigin = 1

prefs = struct with fields:
    FourierParameters: [1/(2*pi)    1]
    HeavisideAtOrigin: 1

sympref(prefs);

Because symbolic settings persist through your current and future MATLAB® sessions, you need to restore your previous settings. Restore the saved settings using sympref(oldPrefs).

sympref(oldPrefs);

Alternatively, you can set all symbolic settings to their default values by specifying the 'default' option.

sympref('default');

Input Arguments

pref — Symbolic setting

character vector | string

Symbolic setting, specified as a character vector or string. The value options for each symbolic setting follow.

setting	Value	Description
'FourierParameters'	Two-element row vector [c,s]. The parameters c and s must be numeric or symbolic numbers. Default: sym([1,-1]).	Set the values of the parameters c and s in the Fourier transform: $$F\left(w\right)=c{\displaystyle \underset{-\infty }{\overset{\infty }{\int }}f\left(t\right)e^{iswt}dt}.$$ See Change Parameter Values of Fourier Transform.
'HeavisideAtOrigin'	Scalar value, specified as a numeric or symbolic number. Default: sym(1/2).	Set the value of the Heaviside function heaviside(0) at the origin. See Change Value of Heaviside Function at Origin.
'AbbreviateOutput'	Logical value (boolean). Default: logical 1 (true).	Specify whether or not to use abbreviated output format of symbolic variables and expressions in Live Scripts. See Modify Display of Symbolic Expressions in Live Scripts.
'TypesetOutput'	Logical value (boolean). Default: logical 1 (true).	Typeset or use ASCII characters for the output of symbolic variables and expressions in Live Scripts. See Modify Display of Symbolic Expressions in Live Scripts.
'FloatingPointOutput'	Logical value (boolean). Default: logical 0 (false).	Specify whether or not to display symbolic results in floating-point output format. The true value option displays symbolic results in the short fixed-decimal format with 4 digits after the decimal point. See Display Symbolic Results in Floating-Point Format.
'PolynomialDisplayStyle'	Character vector or scalar string, specified as 'default', 'ascend', or 'descend'. Default: 'default'.	Display a symbolic polynomial in default, ascending, or descending order. The 'default' option sorts the output in alphabetical order, without distinguishing the different symbolic variables in each monomial term. The 'ascend' option sorts the output in ascending order based on the standard mathematical notation for polynomials. For example, the variable x with the highest order in a monomial term is displayed last, preceded by monomial terms that contain the variables y, z, t, s, and so on. The 'descend' option sorts the output in descending order based on the standard mathematical notation for polynomials. This option is the exact opposite of 'ascend'. See Modify Output Order of Symbolic Polynomial.
'MatrixWithSquareBrackets'	Logical value (boolean). Default: logical 0 (false).	Set matrices in round brackets or parentheses (round brackets) in Live Scripts. See Modify Display of Symbolic Matrix in Live Scripts.

value — Value of symbolic setting

'default' (default) | valid value

Value of symbolic setting, specified as 'default' or a valid value of the specified setting pref.

prefs — Symbolic settings

structure array

Symbolic settings, specified as a structure array. You can set multiple settings by declaring the field names and the valid setting values.

Output Arguments

oldVal — Value of symbolic setting

valid value

Value of symbolic setting, returned as a valid value. oldVal represents the existing value of the setting pref before the call to sympref.

oldPrefs — All symbolic settings

structure array

All symbolic settings, returned as a structure array. oldPrefs represent the existing values of all settings before the call to sympref.

Tips

• The clear command does not reset or affect symbolic settings. Use sympref to manipulate symbolic settings.

• The symbolic settings you set using sympref also determine the output generated by the latex and mathml functions.

• The 'FloatingPointOutput' setting affects only the output display format of symbolic numbers. To change the output display format of numeric numbers, use the format function. To compute symbolic numbers using floating-point precision, use the vpa or digits functions.

Version History

Introduced in R2015a

R2019a: Additional settings to change display of symbolic output

The sympref function accepts the following settings:

• 'FloatingPointOutput' displays symbolic numbers in short fixed-decimal format.

• 'PolynomialDisplayStyle' displays polynomials in ascending or descending order.

• 'MatrixWithSquareBrackets' displays symbolic matrices with square brackets in Live Scripts.