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ginsh(1) The GiNaC Group ginsh(1) NAME ginsh - GiNaC Interactive Shell SYNPOSIS ginsh [file...] DESCRIPTION ginsh is an interactive frontend for the GiNaC symbolic computation frame- work. It is intended as a tool for testing and experimenting with GiNaC's features, not as a replacement for traditional interactive computer algebra systems. Although it can do many things these traditional systems can do, ginsh provides no programming constructs like loops or conditional expres- sions. If you need this functionality you are advised to write your program in C++, using the "native" GiNaC class framework. USAGE INPUT FORMAT 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 expres- sion 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. COMMENTS 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. NUMBERS ginsh accepts numbers in the usual decimal notations. This includes arbi- trary 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 prefix- ing them with #b, #o, #x, or #nR , respectively. SYMBOLS Symbols are made up of a string of alphanumeric characters and the under- score (_), 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. WILDCARDS The has(), find(), match() and subs() functions accept wildcards as place- holders for expressions. These have the syntax $number for example $0, $1 etc. LAST PRINTED EXPRESSIONS ginsh provides the three special symbols %, %% and %%% that refer to the last, second last, and third last printed expression, re- spectively. These are handy if you want to use the results of previous computations in a new expression. OPERATORS ginsh provides the following operators, listed in falling order of prece- dence: ! 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 ex- pression (e.g. a = b = c = 2;). LISTS Lists are used by the subs and lsolve functions. A list consists of an opening curly brace ({), a (possibly empty) comma-separated sequence of ex- pressions, and a closing curly brace (}). MATRICES A matrix consists of an opening square bracket ([), a non-empty comma-sepa- rated sequence of matrix rows, and a closing square bracket (]). Each ma- trix row consists of an opening square bracket ([), a non-empty comma-sepa- rated 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 be- comes that of the longest row and shorter rows are filled up at the end with elements of value zero. FUNCTIONS A function call in ginsh has the form name(arguments) where arguments is a comma-separated sequence of expressions. ginsh pro- vides a couple of built-in functions and also "imports" all symbolic func- tions 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 re- spective GiNaC methods of the same name, so I will not describe them in de- tail here. Please refer to the GiNaC documentation. charpoly(matrix, symbol) - characteristic polynomial of a matrix coeff(expression, object, number) - extracts coefficient of ob- ject^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 evalf(expression) - evaluates an expression to a floating point num- ber evalm(expression) - evaluates sums, products and integer powers of matrices expand(expression) - expands an expression factor(expression) - factorizes an expression (univariate) 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 con- tains 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 equa- tions map(expression, pattern) - apply function to each operand; the func- tion to be applied is specified as a pattern with the "$0" wildcard standing for the operands match(expression, pattern) - check whether expression matches a pat- tern; returns a list of wildcard substitutions or "FAIL" if there is no match nops(expression) - number of operands in expression normal(expression) - 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 polynomi- als 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 polyno- mials with respect to symbol s series(expression, relation-or-symbol, order) - series expansion series_to_poly(series) - convert a series into a polynomial by drop- ping the Order() term sprem(expression, expression, symbol) - sparse pseudo-remainder of polynomials sqrfree(expression [, symbol-list]) - square-free factorization of a polynomial sqrfree_parfrac(expression, symbol) - square-free partial fraction decomposition of rational function sqrt(expression) - square root subs(expression, relation-or-list) subs(expression, look-for-list, replace-by-list) - substitute subex- pressions (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 (mind the quotes, please!) unit(expression, symbol) - unit part of a polynomial SPECIAL COMMANDS 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 expres- sion. 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++ pro- gram. 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 execu- tion. With this method, you can execute shell commands from within ginsh without having to quit. EXAMPLES > a = x^2-x-2; -2-x+x^2 > b = (x+1)^2; (x+1)^2 > s = a/b; (x+1)^(-2)*(-2-x+x^2) > diff(s, x); (2*x-1)*(x+1)^(-2)-2*(x+1)^(-3)*(-x+x^2-2) > normal(s); (x-2)*(x+1)^(-1) > x = 3^50; 717897987691852588770249 > s; 717897987691852588770247/717897987691852588770250 > Digits = 40; 40 > evalf(s); 0.999999999999999999999995821133292704384960990679 > unassign('x'); x > s; (x+1)^(-2)*(-x+x^2-2) > series(sin(x),x==0,6); 1*x+(-1/6)*x^3+1/120*x^5+Order(x^6) > lsolve({3*x+5*y == 7}, {x, y}); {x==-5/3*y+7/3,y==y} > lsolve({3*x+5*y == 7, -2*x+10*y == -5}, {x, y}); {x==19/8,y==-1/40} > M = [ [a, b], [c, d] ]; [[-x+x^2-2,(x+1)^2],[c,d]] > determinant(M); -2*d-2*x*c-x^2*c-x*d+x^2*d-c > collect(%, x); (-d-2*c)*x+(d-c)*x^2-2*d-c > solve quantum field theory; parse error at quantum > quit DIAGNOSTICS parse error at foo You entered something which ginsh was unable to parse. Please check the syntax of your input and try again. argument num to function must be a type The argument number num to the given function must be of a certain type (e.g. a symbol, or a list). The first argument has number 0, the second argument number 1, etc. AUTHOR The GiNaC maintainers <https://www.ginac.de/>. SEE ALSO GiNaC Tutorial - An open framework for symbolic computation within the C++ programming language CLN - A Class Library for Numbers, Bruno Haible COPYRIGHT Copyright (C) 1999-2026 Johannes Gutenberg Universitat Mainz, Germany This program is free software; you can redistribute it and/or modify it un- der the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FIT- NESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with this program. If not, see <https://www.gnu.org/licenses/>. GiNaC 1.8.10 January, 2000 ginsh(1)
NAME | SYNPOSIS | DESCRIPTION | USAGE | EXAMPLES | DIAGNOSTICS | AUTHOR | SEE ALSO | COPYRIGHT
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