1 .TH ginsh 1 "January, 2000" "GiNaC"
3 ginsh \- GiNaC Interactive Shell
9 is an interactive frontend for the GiNaC symbolic computation framework.
10 It is intended as a tool for testing and experimenting with GiNaC's
11 features, not as a replacement for traditional interactive computer
12 algebra systems. Although it can do many things these traditional systems
13 can do, ginsh provides no programming constructs like loops or conditional
14 expressions. If you need this functionality you are advised to write
15 your program in C++, using the "native" GiNaC class framework.
18 After startup, ginsh displays a prompt ("> ") signifying that it is ready
19 to accept your input. Acceptable input are numeric or symbolic expressions
20 consisting of numbers (e.g.
21 .BR 42 ", " 2/3 " or " 0.17 ),
23 .BR x " or " result ),
24 mathematical operators like
27 .BR sin " or " normal ).
28 Every input expression must be terminated with either a semicolon
32 If terminated with a semicolon, ginsh will evaluate the expression and print
33 the result to stdout. If terminated with a colon, ginsh will only evaluate the
34 expression but not print the result. It is possible to enter multiple
35 expressions on one line. Whitespace (spaces, tabs, newlines) can be applied
36 freely between tokens. To quit ginsh, enter
37 .BR quit " or " exit ,
38 or type an EOF (Ctrl-D) at the prompt.
40 Anything following a double slash
42 up to the end of the line, and all lines starting with a hash mark
44 are treated as a comment and ignored.
46 ginsh accepts numbers in the usual decimal notations. This includes arbitrary
47 precision integers and rationals as well as floating point numbers in standard
48 or scientific notation (e.g.
50 The general rule is that if a number contains a decimal point
52 it is an (inexact) floating point number; otherwise it is an (exact) integer or
54 Integers can be specified in binary, octal, hexadecimal or arbitrary (2-36) base
55 by prefixing them with
56 .BR #b ", " #o ", " #x ", or "
60 Symbols are made up of a string of alphanumeric characters and the underscore
62 with the first character being non-numeric. E.g.
64 are acceptable symbol names, while
66 is not. It is possible to use symbols with the same names as functions (e.g.
68 ginsh is able to distinguish between the two.
70 Symbols can be assigned values by entering
72 .IB symbol " = " expression ;
75 To unassign the value of an assigned symbol, type
77 .BI unassign(' symbol ');
80 Assigned symbols are automatically evaluated (= replaced by their assigned value)
81 when they are used. To refer to the unevaluated symbol, put single quotes
83 around the name, as demonstrated for the "unassign" command above.
85 The following symbols are pre-defined constants that cannot be assigned
96 Euler-Mascheroni Constant
102 an object of the GiNaC "fail" class
105 There is also the special
109 symbol that controls the numeric precision of calculations with inexact numbers.
110 Assigning an integer value to digits will change the precision to the given
111 number of decimal places.
112 .SS LAST PRINTED EXPRESSIONS
113 ginsh provides the three special symbols
117 that refer to the last, second last, and third last printed expression, respectively.
118 These are handy if you want to use the results of previous computations in a new
121 ginsh provides the following operators, listed in falling order of precedence:
124 \" GINSH_OP_HELP_START
141 non-commutative multiplication
175 All binary operators are left-associative, with the exception of
177 which are right-associative. The result of the assignment operator
179 is its right-hand side, so it's possible to assign multiple symbols in one
181 .BR "a = b = c = 2;" ).
183 Lists are used by the
187 functions. A list consists of an opening square bracket
189 a (possibly empty) comma-separated sequence of expressions, and a closing square
193 A matrix consists of an opening double square bracket
195 a non-empty comma-separated sequence of matrix rows, and a closing double square
198 Each matrix row consists of an opening double square bracket
200 a non-empty comma-separated sequence of expressions, and a closing double square
203 If the rows of a matrix are not of the same length, the width of the matrix
204 becomes that of the longest row and shorter rows are filled up at the end
205 with elements of value zero.
207 A function call in ginsh has the form
209 .IB name ( arguments )
213 is a comma-separated sequence of expressions. ginsh provides a couple of built-in
214 functions and also "imports" all symbolic functions defined by GiNaC and additional
215 libraries. There is no way to define your own functions other than linking ginsh
216 against a library that defines symbolic GiNaC functions.
218 ginsh provides Tab-completion on function names: if you type the first part of
219 a function name, hitting Tab will complete the name if possible. If the part you
220 typed is not unique, hitting Tab again will display a list of matching functions.
221 Hitting Tab twice at the prompt will display the list of all available functions.
223 A list of the built-in functions follows. They nearly all work as the
224 respective GiNaC methods of the same name, so I will not describe them in
225 detail here. Please refer to the GiNaC documentation.
228 \" GINSH_FCN_HELP_START
229 .BI charpoly( matrix ", " symbol )
230 \- characteristic polynomial of a matrix
232 .BI coeff( expression ", " symbol ", " number )
233 \- extracts coefficient of symbol^number from a polynomial
235 .BI collect( expression ", " symbol )
236 \- collects coefficients of like powers
238 .BI content( expression ", " symbol )
239 \- content part of a polynomial
241 .BI degree( expression ", " symbol )
242 \- degree of a polynomial
244 .BI denom( expression )
245 \- denominator of a rational function
247 .BI determinant( matrix )
248 \- determinant of a matrix
250 .BI diag( expression... )
251 \- constructs diagonal matrix
253 .BI diff( expression ", " "symbol [" ", " number] )
254 \- partial differentiation
256 .BI divide( expression ", " expression )
257 \- exact polynomial division
259 .BI eval( "expression [" ", " level] )
260 \- evaluates an expression, replacing symbols by their assigned value
262 .BI evalf( "expression [" ", " level] )
263 \- evaluates an expression to a floating point number
265 .BI expand( expression )
266 \- expands an expression
268 .BI gcd( expression ", " expression )
269 \- greatest common divisor
271 .BI has( expression ", " expression )
272 \- returns "1" if the first expression contains the second as a subexpression, "0" otherwise
274 .BI inverse( matrix )
275 \- inverse of a matrix
278 \- returns "1" if the relation is true, "0" otherwise (false or undecided)
280 .BI lcm( expression ", " expression )
281 \- least common multiple
283 .BI lcoeff( expression ", " symbol )
284 \- leading coefficient of a polynomial
286 .BI ldegree( expression ", " symbol )
287 \- low degree of a polynomial
289 .BI lsolve( equation-list ", " symbol-list )
290 \- solve system of linear equations
292 .BI nops( expression )
293 \- number of operands in expression
295 .BI normal( "expression [" ", " level] )
296 \- rational function normalization
298 .BI numer( expression )
299 \- numerator of a rational function
301 .BI op( expression ", " number )
302 \- extract operand from expression
304 .BI power( expr1 ", " expr2 )
305 \- exponentiation (equivalent to writing expr1^expr2)
307 .BI prem( expression ", " expression ", " symbol )
308 \- pseudo-remainder of polynomials
310 .BI primpart( expression ", " symbol )
311 \- primitive part of a polynomial
313 .BI quo( expression ", " expression ", " symbol )
314 \- quotient of polynomials
316 .BI rem( expression ", " expression ", " symbol )
317 \- remainder of polynomials
319 .BI series( expression ", " relation-or-symbol ", " order )
322 .BI sqrfree( expression ", " symbol )
323 \- square-free factorization of a polynomial
325 .BI sqrt( expression )
328 .BI subs( expression ", " relation-or-list )
330 .BI subs( expression ", " look-for-list ", " replace-by-list )
331 \- substitute subexpressions
333 .BI tcoeff( expression ", " symbol )
334 \- trailing coefficient of a polynomial
336 .BI time( expression )
337 \- returns the time in seconds needed to evaluate the given expression
342 .BI transpose( matrix )
343 \- transpose of a matrix
345 .BI unassign( symbol )
346 \- unassign an assigned symbol
348 .BI unit( expression ", " symbol )
349 \- unit part of a polynomial
351 \" GINSH_FCN_HELP_END
363 ginsh can display a (short) help for a given topic (mostly about functions
364 and operators) by entering
372 will display a list of available help topics.
376 .BI print( expression );
378 will print a dump of GiNaC's internal representation for the given
380 This is useful for debugging and for learning about GiNaC internals.
384 .BI iprint( expression );
388 (which must evaluate to an integer) in decimal, octal, and hexadecimal representations.
390 Finally, the shell escape
393 .RI [ "command " [ arguments ]]
399 to the shell for execution. With this method, you can execute shell commands
400 from within ginsh without having to quit.
408 (x+1)^(\-2)*(\-x+x^2\-2)
410 (2*x\-1)*(x+1)^(\-2)\-2*(x+1)^(\-3)*(\-x+x^2\-2)
414 717897987691852588770249
416 717897987691852588770247/717897987691852588770250
420 0.999999999999999999999995821133292704384960990679L0
424 (x+1)^(\-2)*(\-x+x^2\-2)
425 > lsolve([3*x+5*y == 7], [x, y]);
426 [x==\-5/3*y+7/3,y==y]
427 > lsolve([3*x+5*y == 7, \-2*x+10*y == \-5], [x, y]);
429 > M = [[ [[a, b]], [[c, d]] ]];
430 [[ [[\-x+x^2\-2,(x+1)^2]], [[c,d]] ]]
432 \-2*d\-2*x*c\-x^2*c\-x*d+x^2*d\-c
434 (\-d\-2*c)*x+(d\-c)*x^2\-2*d\-c
435 > solve quantum field theory;
436 parse error at quantum
441 .RI "parse error at " foo
442 You entered something which ginsh was unable to parse. Please check the syntax
443 of your input and try again.
445 .RI "argument " num " to " function " must be a " type
450 must be of a certain type (e.g. a symbol, or a list). The first argument has
451 number 0, the second argument number 1, etc.
456 Christian Bauer <Christian.Bauer@uni-mainz.de>
458 Alexander Frink <Alexander.Frink@uni-mainz.de>
460 Richard Kreckel <Richard.Kreckel@uni-mainz.de>
462 GiNaC Tutorial \- An open framework for symbolic computation within the
463 C++ programming language
465 CLN \- A Class Library for Numbers, Bruno Haible
467 Copyright \(co 1999-2000 Johannes Gutenberg Universit\(:at Mainz, Germany
469 This program is free software; you can redistribute it and/or modify
470 it under the terms of the GNU General Public License as published by
471 the Free Software Foundation; either version 2 of the License, or
472 (at your option) any later version.
474 This program is distributed in the hope that it will be useful,
475 but WITHOUT ANY WARRANTY; without even the implied warranty of
476 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
477 GNU General Public License for more details.
479 You should have received a copy of the GNU General Public License
480 along with this program; if not, write to the Free Software
481 Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.