Is exp() a Documented Function in the Symbolic Math Toolbox?

I can't find it.

[Sam Chak]

I think you already know that exp(x), like sin(x) and cos(x), is a transcendental function. They are under elementary math.

So, I am wondering if you want to define the exponential function symbolically.

[Paul]

It is defined for symbolic inputs and, i would imagine, commonly used. sin(), cos(), log(), etc. are implemented and documented. Seems strange that exp() is not.

[Sam Chak]

Yes, it's strange. Even symbolic log(X) is documented.

https://www.mathworks.com/help/symbolic/mathematical-functions.html

syms x
y = cos(x)
x = pi;
subs(y)

ans =

-1

syms x
y = exp(x)
x = pi;
subs(y)

ans =

exp(pi)

Answer 1

[Steven Lord]

There is no separate documentation page for the exp method for sym objects, this is true. Not all methods of classes have documentation pages, and I believe this is especially true if the methods have very similar or the same behavior as the versions of the functions for double and single precision data. In fact if you look at the list of function reference pages for exp that appear on the first page of a search, the only three that show up are the double/single precision version in MATLAB, the quaternion version in a number of different toolboxes, and the fints version in Financial Toolbox (which is discouraged because fints is discouraged, with timetable being the recommended replacement.) There are more than just those three overloads.

which -all exp

built-in (/MATLAB/toolbox/matlab/elfun/@double/exp)     % double method
built-in (/MATLAB/toolbox/matlab/elfun/@single/exp)     % Shadowed single method
exp is a built-in method                                % Shadowed matlab.unittest.Verbosity method
exp is a built-in method                                % Shadowed matlab.unittest.internal.fixtures.FolderScope method
/MATLAB/toolbox/coder/half/@bfloat16/exp.p              % Shadowed bfloat16 method
/MATLAB/toolbox/control/ctrlmodels/@zpk/exp.m           % Shadowed zpk method
/MATLAB/toolbox/control/ctrlmodels/@tf/exp.m            % Shadowed tf method
/MATLAB/toolbox/finance/ftseries/@fints/exp.m           % Shadowed fints method
/MATLAB/toolbox/nnet/deep/@dlarray/exp.m                % Shadowed dlarray method
/MATLAB/toolbox/parallel/gpu/@gpuArray/exp.m            % Shadowed gpuArray method
/MATLAB/toolbox/parallel/parallel/@codistributed/exp.m  % Shadowed codistributed method
/MATLAB/toolbox/symbolic/symbolic/@sym/exp.m            % Shadowed sym method

If you want to see the operations defined for sym objects you can ask MATLAB what methods are defined for that class. Note that this doesn't list all the operations you can perform on sym objects, as some MATLAB functions will operate on instances of a class as long as all the operations the function uses work on that class. For example the var function is not overloaded for sym but because all of the functions var.m uses work for sym you can compute the var of a symbolic vector.

which -all var % No sym overload

/MATLAB/toolbox/matlab/datafun/var.m
/MATLAB/toolbox/matlab/timeseries/@timeseries/var.m     % Shadowed timeseries method
/MATLAB/toolbox/matlab/bigdata/@tall/var.m              % Shadowed tall method
/MATLAB/toolbox/finance/ftseries/@fints/var.m           % Shadowed fints method
/MATLAB/toolbox/parallel/gpu/@gpuArray/var.m            % Shadowed gpuArray method
/MATLAB/toolbox/parallel/parallel/@codistributed/var.m  % Shadowed codistributed method

var(1:5)

ans = 2.5000

var(sym(1:5)) % But it works

ans = 

methods sym

Methods for class sym:

abs                        compose                    erfinv                     hypot                      laplacian                  permute                    sinint                     
acos                       cond                       euler                      ifourier                   latex                      piecewise                  sinpi                      
acosd                      conj                       eval                       igamma                     lcm                        pinv                       size                       
acosh                      cos                        exp                        ihtrans                    ldivide                    plus                       solve                      
acot                       cosd                       expand                     ilaplace                   le                         pochhammer                 sort                       
acotd                      cosh                       expint                     imag                       legendreP                  poles                      sqrt                       
acoth                      coshint                    expm                       in                         length                     poly                       sqrtm                      
acsc                       cosint                     ezcontour                  incidenceMatrix            lhs                        poly2sym                   ssinint                    
acscd                      cospi                      ezcontourf                 inline                     limit                      polylog                    string                     
acsch                      cot                        ezmesh                     int                        linsolve                   polynomialDegree           subexpr                    
adjoint                    cotd                       ezmeshc                    int16                      log                        polynomialReduce           subs                       
airy                       coth                       ezplot                     int32                      log10                      potential                  sum                        
all                        csc                        ezplot3                    int64                      log2                       power                      svd                        
and                        cscd                       ezpolar                    int8                       logical                    powermod                   sym                        
angle                      csch                       ezsurf                     integrateByParts           logint                     pretty                     sym2cell                   
any                        ctranspose                 ezsurfc                    inv                        logm                       prevprime                  sym2poly                   
argnames                   cumprod                    factor                     isAlways                   lt                         prod                       symFunType                 
asec                       cumsum                     factorIntegerPower         isLowIndexDAE              lu                         psi                        symType                    
asecd                      curl                       factorial                  isSymType                  mapSymType                 qr                         symprod                    
asech                      daeFunction                fibonacci                  isempty                    massMatrixForm             quorem                     symsum                     
asin                       dawson                     find                       isequal                    mathml                     rad2deg                    symvar                     
asind                      dec2bin                    findDecoupledBlocks        isequaln                   matlabFunction             rank                       tan                        
asinh                      dec2hex                    findSymType                isfinite                   matlabFunctionBlock        rat                        tand                       
assume                     decic                      finverse                   isinf                      max                        rdivide                    tanh                       
assumeAlso                 deg2rad                    fix                        ismember                   meijerG                    real                       taylor                     
atan                       delete                     floor                      ismissing                  min                        rectangularPulse           texlabel                   
atan2                      det                        formula                    isnan                      minpoly                    reduceDAEIndex             times                      
atan2d                     diag                       fortran                    isolate                    minus                      reduceDAEToODE             toeplitz                   
atand                      diff                       fourier                    isprime                    mixedUnits                 reduceDifferentialOrder    transpose                  
atanh                      dilog                      frac                       isreal                     mldivide                   reduceRedundancies         triangularPulse            
bernoulli                  dirac                      fresnelc                   isscalar                   mod                        release                    tril                       
bernstein                  disp                       fresnels                   iztrans                    mpower                     rem                        triu                       
bernsteinMatrix            display                    full                       jacobiAM                   mrdivide                   reshape                    uint16                     
besselh                    divergence                 functionalDerivative       jacobiCD                   mtimes                     resultant                  uint32                     
besseli                    divisors                   funm                       jacobiCN                   mustBeInteger              rhs                        uint64                     
besselj                    double                     gamma                      jacobiCS                   mustBePositive             root                       uint8                      
besselk                    ei                         gammaln                    jacobiDC                   nchoosek                   round                      uminus                     
bessely                    eig                        gbasis                     jacobiDN                   ndims                      rref                       unique                     
beta                       eliminate                  gcd                        jacobiDS                   ne                         rsums                      uplus                      
cat                        ellipj                     ge                         jacobiNC                   nextprime                  saveobj                    vectorPotential            
ccode                      ellipke                    gegenbauerC                jacobiND                   nnz                        sec                        vertcat                    
ceil                       ellipticCE                 gradient                   jacobiNS                   nonzeros                   secd                       vpa                        
changeIntegrationVariable  ellipticCK                 gt                         jacobiP                    norm                       sech                       vpaintegral                
char                       ellipticCPi                half                       jacobiSC                   not                        series                     vpasolve                   
charpoly                   ellipticE                  harmonic                   jacobiSD                   nthroot                    sign                       vpasum                     
chebyshevT                 ellipticF                  has                        jacobiSN                   null                       signIm                     whittakerM                 
chebyshevU                 ellipticK                  hasSymType                 jacobiZeta                 numden                     simplify                   whittakerW                 
checkUnits                 ellipticNome               heaviside                  jacobian                   numel                      simplifyFraction           wrightOmega                
children                   ellipticPi                 hermiteH                   jordan                     odeFunction                simscapeEquation           xor                        
chol                       eq                         hessian                    kron                       or                         sin                        zeta                       
coeffs                     equationsToMatrix          horner                     kroneckerDelta             orth                       sinc                       ztrans                     
collect                    erf                        horzcat                    kummerU                    pade                       sind                       
colon                      erfc                       htrans                     laguerreL                  partfrac                   single                     
colspace                   erfcinv                    hurwitzZeta                lambertw                   pdeCoefficients            sinh                       
combine                    erfi                       hypergeom                  laplace                    perms                      sinhint                    

Static methods:

cast                       eye                        loadobj                    ones                       
empty                      inf                        nan                        zeros                      

Call "methods('handle')" for methods of sym inherited from handle.

[Paul]

@Steven Lord

Thanks for the comprehensive answer. Any idea why symbolic log() has a doc page and exp() does not?

The more I think about it, the more suprised I am that sym exp() is not in the doc. For me, when I'm trying to learn how to use a toolbox, I go to the doc and start clicking around, particularly on the "Functions" at the top of a page, and when I do expect to see a comprehensive list of applicable functions, organized by group, etc. I would never use methods() at the command line.

I realize that there will always be functions like var(), but that's a different situation IMO.

Answer 2

[Image Analyst]

Type

which -all exp

to find out.

[Paul]

which() only indicates that an item is found, not whether or not it's documented.

But I've also run across the opposite. For example, the function eul2rotm() can be found in the doc in multiple toolboxes:

eul2rotm, eul2rotm, eul2rotm

But which() only returns one instance:

which eul2rotm -all

/MATLAB/toolbox/shared/robotics/robotutils/eul2rotm.m

Answer 3

[Walter Roberson]

There is no doc for it.

help sym/exp

gives very brief help (nearly useless)

[Paul]

"very brief" is being kind. exp(sym) not being documented is ... odd. I mean of all the implemented functions I would think exp() would be one of the least likely to be not documented.

BTW, I stumbled on this using the new @doc thing here to generate a link to the symbolic version of exp() and was flummoxed when it didn't show up on the list.