After startup, ginsh displays a prompt ("> ") signifying that it is ready to accept your input. Acceptable input are numeric or symbolic expressions consisting of numbers (e.g. 42, 2/3 or 0.17), symbols (e.g. x or result), mathematical operators like + and *, and functions (e.g. sin or normal). Every input expression must be terminated with either a semicolon (;) or a colon (:). If terminated with a semicolon, ginsh will evaluate the expression and print the result to stdout. If terminated with a colon, ginsh will only evaluate the expression but not print the result. It is possible to enter multiple expressions on one line. Whitespace (spaces, tabs, newlines) can be applied freely between tokens. To quit ginsh, enter quit or exit, or type an EOF (Ctrl-D) at the prompt.

Anything following a double slash (//) up to the end of the line, and all lines starting with a hash mark (#) are treated as a comment and ignored.

ginsh accepts numbers in the usual decimal notations. This includes arbitrary precision integers and rationals as well as floating point numbers in standard or scientific notation (e.g. 1.2E6). The general rule is that if a number contains a decimal point (.), it is an (inexact) floating point number; otherwise it is an (exact) integer or rational. Integers can be specified in binary, octal, hexadecimal or arbitrary (2-36) base by prefixing them with #b, #o, #x, or #nR , respectively.

Symbols are made up of a string of alphanumeric characters and the underscore (_), with the first character being non-numeric. E.g. a and mu_1 are acceptable symbol names, while 2pi is not. It is possible to use symbols with the same names as functions (e.g. sin); ginsh is able to distinguish between the two.

Symbols can be assigned values by entering symbol = expression;

To unassign the value of an assigned symbol, type unassign('symbol');

Assigned symbols are automatically evaluated (= replaced by their assigned value) when they are used. To refer to the unevaluated symbol, put single quotes (') around the name, as demonstrated for the "unassign" command above.

Symbols are considered to be in the complex domain by default, i.e. they are treated as if they stand in for complex numbers. This behavior can be changed by using the keywords real_symbols and complex_symbols and affects all newly created symbols.

The following symbols are pre-defined constants that cannot be assigned a value by the user:

Pi

Archimedes' Constant

Catalan

Catalan's Constant

Euler

Euler-Mascheroni Constant

I

sqrt(-1)

FAIL

an object of the GiNaC "fail" class

There is also the special Digits symbol that controls the numeric precision of calculations with inexact numbers. Assigning an integer value to digits will change the precision to the given number of decimal places.

The has(), find(), match() and subs() functions accept wildcards as placeholders for expressions. These have the syntax $number for example $0, $1 etc.

ginsh provides the three special symbols %, %% and %%% that refer to the last, second last, and third last printed expression, respectively. These are handy if you want to use the results of previous computations in a new expression.

ginsh provides the following operators, listed in falling order of precedence:

! postfix factorial

^

powering

+

unary plus

-

unary minus

*

multiplication

/

division

+

addition

-

subtraction

<

less than

>

greater than

<=

less or equal

>=

greater or equal

==

equal

!=

not equal

=

symbol assignment

All binary operators are left-associative, with the exception of ^ and = which are right-associative. The result of the assignment operator (=) is its right-hand side, so it's possible to assign multiple symbols in one expression (e.g. a = b = c = 2;).

Lists are used by the subs and lsolve functions. A list consists of an opening curly brace ({), a (possibly empty) comma-separated sequence of expressions, and a closing curly brace (}).

A matrix consists of an opening square bracket ([), a non-empty comma-separated sequence of matrix rows, and a closing square bracket (]). Each matrix row consists of an opening square bracket ([), a non-empty comma-separated sequence of expressions, and a closing square bracket (]). If the rows of a matrix are not of the same length, the width of the matrix becomes that of the longest row and shorter rows are filled up at the end with elements of value zero.

A function call in ginsh has the form name(arguments) where arguments is a comma-separated sequence of expressions. ginsh provides a couple of built-in functions and also "imports" all symbolic functions defined by GiNaC and additional libraries. There is no way to define your own functions other than linking ginsh against a library that defines symbolic GiNaC functions.

ginsh provides Tab-completion on function names: if you type the first part of a function name, hitting Tab will complete the name if possible. If the part you typed is not unique, hitting Tab again will display a list of matching functions. Hitting Tab twice at the prompt will display the list of all available functions.

A list of the built-in functions follows. They nearly all work as the respective GiNaC methods of the same name, so I will not describe them in detail here. Please refer to the GiNaC documentation.

charpoly(matrix, symbol) - characteristic polynomial of a matrix

coeff(expression, object, number) - extracts coefficient of object^number from a polynomial

collect(expression, object-or-list) - collects coefficients of like powers (result in recursive form)

collect_distributed(expression, list) - collects coefficients of like powers (result in distributed form)

collect_common_factors(expression) - collects common factors from the terms of sums

conjugate(expression) - complex conjugation

content(expression, symbol) - content part of a polynomial

decomp_rational(expression, symbol) - decompose rational function into polynomial and proper rational function

degree(expression, object) - degree of a polynomial

denom(expression) - denominator of a rational function

determinant(matrix) - determinant of a matrix

diag(expression...) - constructs diagonal matrix

diff(expression, symbol [, number]) - partial differentiation

divide(expression, expression) - exact polynomial division

eval(expression [, level]) - evaluates an expression, replacing symbols by their assigned value

evalf(expression [, level]) - evaluates an expression to a floating point number

evalm(expression) - evaluates sums, products and integer powers of matrices

expand(expression) - expands an expression

find(expression, pattern) - returns a list of all occurrences of a pattern in an expression

fsolve(expression, symbol, number, number) - numerically find root of a real-valued function within an interval

gcd(expression, expression) - greatest common divisor

has(expression, pattern) - returns "1" if the first expression contains the pattern as a subexpression, "0" otherwise

integer_content(expression) - integer content of a polynomial

inverse(matrix) - inverse of a matrix

is(relation) - returns "1" if the relation is true, "0" otherwise (false or undecided)

lcm(expression, expression) - least common multiple

lcoeff(expression, object) - leading coefficient of a polynomial

ldegree(expression, object) - low degree of a polynomial

lsolve(equation-list, symbol-list) - solve system of linear equations

map(expression, pattern) - apply function to each operand; the function to be applied is specified as a pattern with the "$0" wildcard standing for the operands

match(expression, pattern) - check whether expression matches a pattern; returns a list of wildcard substitutions or "FAIL" if there is no match

nops(expression) - number of operands in expression

normal(expression [, level]) - rational function normalization

numer(expression) - numerator of a rational function

numer_denom(expression) - numerator and denumerator of a rational function as a list

op(expression, number) - extract operand from expression

power(expr1, expr2) - exponentiation (equivalent to writing expr1^expr2)

prem(expression, expression, symbol) - pseudo-remainder of polynomials

primpart(expression, symbol) - primitive part of a polynomial

quo(expression, expression, symbol) - quotient of polynomials

rank(matrix) - rank of a matrix

rem(expression, expression, symbol) - remainder of polynomials

resultant(expression, expression, symbol) - resultant of two polynomials with respect to symbol s

series(expression, relation-or-symbol, order) - series expansion

sprem(expression, expression, symbol) - sparse pseudo-remainder of polynomials

sqrfree(expression [, symbol-list]) - square-free factorization of a polynomial

sqrt(expression) - square root

subs(expression, relation-or-list)

subs(expression, look-for-list, replace-by-list) - substitute subexpressions (you may use wildcards)

tcoeff(expression, object) - trailing coefficient of a polynomial

time(expression) - returns the time in seconds needed to evaluate the given expression

trace(matrix) - trace of a matrix

transpose(matrix) - transpose of a matrix

unassign(symbol) - unassign an assigned symbol

unit(expression, symbol) - unit part of a polynomial

To exit ginsh, enter quit or exit

ginsh can display a (short) help for a given topic (mostly about functions and operators) by entering ?topic Typing ?? will display a list of available help topics.

The command print(expression); will print a dump of GiNaC's internal representation for the given expression. This is useful for debugging and for learning about GiNaC internals.

The command print_latex(expression); prints a LaTeX representation of the given expression.

The command print_csrc(expression); prints the given expression in a way that can be used in a C or C++ program.

The command iprint(expression); prints the given expression (which must evaluate to an integer) in decimal, octal, and hexadecimal representations.

Finally, the shell escape ! [command [arguments]] passes the given command and optionally arguments to the shell for execution. With this method, you can execute shell commands from within ginsh without having to quit.