The Octave Symbolic Manipulation Toolbox is based upon  GiNaC .   The goal is to simply provide the capabilities of GiNaC in the easy to use environment provided by Octave.

Limitations/Features
Currently there is no support for symbolic matrices. I think it would require a few changes to the parser to do it nicely: for example:  sym_matrix = [x+1, x+5; x^2+4,x^2+2*x+1];  I could make a function like sym_matrix(the_rows,the_columns,x+1, ... )  that returned a symbolic matrix but this would be a bit of a kludge.

In order to do exact arithmetic you need to deal with strings and the vpa command.  For example:  vpa("1")/vpa("7") is represented internally as exactly 1/7.   However,  vpa("1")/7 or 1/vpa("7")  is an approximation to 1/7 that is accurate to roughly the accuracy of the current value of digits.

GiNaC throws exceptions when there are problems with computations.   I handle some of them at this time, but I do not handle all of them.   This can cause octave to terminate prematurely.   For example, try vpa("1")/vpa("0").   This will eventually be fixed.

Download and install

You will need to install cln-1.0.1, GiNaC-0.8.0 and octave-2.1.33 or later to use this package.  You may be able to get by with an earlier version of octave if you compiled without the "-fno-rtti -fno-exceptions" options.   This package uses both exceptions and run-time type identification.    There is an INSTALL file in the package which will tell you how to install the package.

Functions
Below I provide a list of function that I have implemented or have plans to implement as of the latest release .  If the function name is green then the function is implemented and to the best of my knowledge there are no problems with it.  If the function is red then it has not been implemented yet.  If the function is blue then it has been implemented but is known not to work correctly.  Blues will appear only very rarely.

• vpa  - create a variable precision arithmetic variable from a string, double, or an appropriate expression.
• sym  - create a symbolic variable
• is_vpa  - returns true if an object is a vpa object
• is_sym  - return true if the argument is a symbolic variable
• is_ex  - returns true if an object a symbolic expression (i.e.  x+y)
• to_double  - convert a vpa, ex or string to a double value.
• to_char  - convert a vpa, ex to a string.
• digits  - set or view the number of digits that newly created vpa object should have
• Abs  - Absolute value
• csgn  -
• Sqrt  - Sqrt(x)  => x^(vpa(1)/2) or x^(1/vpa(2))
• Cos  - the cosine of a sym, vpa , or ex variable
• Sin - the sine of a sym, vpa , or ex variable
• Tan - the tangent of a sym, vpa , or ex variable
• aCos  - the inverse cosine of a sym, vpa , or ex variable
• aSin  - the inverse sin of a sym, vpa , or ex variable
• aTan  - the inverse tangent of a sym, vpa , or ex variable
• aTan2  -
• Cosh  - the hyperbolic cosine of a sym, vpa , or ex variable
• Sinh  - the hyperbolic sine of a sym, vpa , or ex variable
• Tanh  - the hyperbolic tangent of a sym, vpa , or ex variable
• aCosh - the inverse hyperbolic cosine of a sym, vpa , or ex variable
• aSinh - the inverse hyperbolic sine of a sym, vpa , or ex variable
• aTanh  - the inverse hyperbolic tangent of a sym, vpa , or ex variable
• Exp  - the cosine of a sym, vpa , or ex variable
• Log  - the cosine of a sym, vpa , or ex variable
• Zeta  -
• Tgamma  -
• Lgamma  -
• Beta  -
• Factorial  -
• Binomial  -
• Order -
• subs - perform a substitution in an expression
• differentiate  - differentiate an expression
• expand  -  multiply all of the terms in an expression out:  (x+y)*(x+z) => x^2+x*y+x*z+y*z
• collect  - collect similar terms in an already expanded expression
• coeff  - return the nth coefficient in a polynomial
• lcoeff  - leading coefficient of a polynomial (4x^2+2x+5 => 4)
• tcoeff  - trailing coefficient of a polynomial (4x^2+2x+5 => 5)
• degree  - The degree of a polynomial (i.e. x^2+2x+1 => 2)
• ldegree  - The low degree of a polynomial (i.e. x^2+2x+1  => 0)
• quotient  -
• remainder  -
• premainder  -
• unit  -
• content  -
• primpart  -
• Gcd  - greatest common denominator of a polynomial expression
• Lcm  - least common multiple of a polynomial expression
• numer  -
• denom  -
• normal  - ?
• to_rational  -
• Series  -
• Pi  - pi evaluated to the current value of digits accuracy.
• splot  -plot a symbolic functin over a range of values
• Saving of expressions, Retrieving of expressions