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 is treated as a comment and ignored.
44 ginsh accepts numbers in the usual decimal notations. This includes arbitrary
45 precision integers and rationals as well as floating point numbers in standard
46 or scientific notation (e.g.
48 The general rule is that if a number contains a decimal point
50 it is an (inexact) floating point number; otherwise it is an (exact) integer or
52 Integers can be specified in binary, octal, hexadecimal or arbitrary (2-36) base
53 by prefixing them with
54 .BR #b ", " #o ", " #x ", or "
58 Symbols are made up of a string of alphanumeric characters and the underscore
60 with the first character being non-numeric. E.g.
62 are acceptable symbol names, while
64 is not. It is possible to use symbols with the same names as functions (e.g.
66 ginsh is able to distinguish between the two.
68 Symbols can be assigned values by entering
70 .IB symbol " = " expression ;
73 To unassign the value of an assigned symbol, type
75 .BI unassign(' symbol ');
78 Assigned symbols are automatically evaluated (= replaced by their assigned value)
79 when they are used. To refer to the unevaluated symbol, put single quotes
81 around the name, as demonstrated for the "unassign" command above.
83 The following symbols are pre-defined constants that cannot be assigned
94 Euler-Mascheroni Constant
100 an object of the GiNaC "fail" class
103 There is also the special
107 symbol that controls the numeric precision of calculations with inexact numbers.
108 Assigning an integer value to digits will change the precision to the given
109 number of decimal places.
110 .SS LAST PRINTED EXPRESSIONS
111 ginsh provides the three special symbols
115 that refer to the last, second last, and third last printed expression, respectively.
116 These are handy if you want to use the results of previous computations in a new
119 ginsh provides the following operators, listed in falling order of precedence:
122 \" GINSH_OP_HELP_START
139 non-commutative multiplication
173 All binary operators are left-associative, with the exception of
175 which are right-associative. The result of the assignment operator
177 is its right-hand side, so it's possible to assign multiple symbols in one
179 .BR "a = b = c = 2;" ).
181 Lists are used by the
185 functions. A list consists of an opening square bracket
187 a (possibly empty) comma-separated sequence of expressions, and a closing square
191 A matrix consists of an opening double square bracket
193 a non-empty comma-separated sequence of matrix rows, and a closing double square
196 Each matrix row consists of an opening double square bracket
198 a non-empty comma-separated sequence of expressions, and a closing double square
201 If the rows of a matrix are not of the same length, the width of the matrix
202 becomes that of the longest row and shorter rows are filled up at the end
203 with elements of value zero.
205 A function call in ginsh has the form
207 .IB name ( arguments )
211 is a comma-separated sequence of expressions. ginsh provides a couple of built-in
212 functions and also "imports" all symbolic functions defined by GiNaC and additional
213 libraries. There is no way to define your own functions other than linking ginsh
214 against a library that defines symbolic GiNaC functions.
216 ginsh provides Tab-completion on function names: if you type the first part of
217 a function name, hitting Tab will complete the name if possible. If the part you
218 typed is not unique, hitting Tab again will display a list of matching functions.
219 Hitting Tab twice at the prompt will display the list of all available functions.
221 A list of the built-in functions follows. They nearly all work as the
222 respective GiNaC methods of the same name, so I will not describe them in
223 detail here. Please refer to the GiNaC documentation.
226 \" GINSH_FCN_HELP_START
227 .BI charpoly( matrix ", " symbol )
228 \- characteristic polynomial of a matrix
230 .BI coeff( expression ", " symbol ", " number )
231 \- extracts coefficient of symbol^number from a polynomial
233 .BI collect( expression ", " symbol )
234 \- collects coefficients of like powers
236 .BI content( expression ", " symbol )
237 \- content part of a polynomial
239 .BI degree( expression ", " symbol )
240 \- degree of a polynomial
242 .BI denom( expression )
243 \- denominator of a rational function
245 .BI determinant( matrix )
246 \- determinant of a matrix
248 .BI diag( expression... )
249 \- constructs diagonal matrix
251 .BI diff( expression ", " "symbol [" ", " number] )
252 \- partial differentiation
254 .BI divide( expression ", " expression )
255 \- exact polynomial division
257 .BI eval( "expression [" ", " level] )
258 \- evaluates an expression, replacing symbols by their assigned value
260 .BI evalf( "expression [" ", " level] )
261 \- evaluates an expression to a floating point number
263 .BI expand( expression )
264 \- expands an expression
266 .BI gcd( expression ", " expression )
267 \- greatest common divisor
269 .BI has( expression ", " expression )
270 \- returns "1" if the first expression contains the second as a subexpression, "0" otherwise
272 .BI inverse( matrix )
273 \- inverse of a matrix
276 \- returns "1" if the relation is true, "0" otherwise (false or undecided)
278 .BI lcm( expression ", " expression )
279 \- least common multiple
281 .BI lcoeff( expression ", " symbol )
282 \- leading coefficient of a polynomial
284 .BI ldegree( expression ", " symbol )
285 \- low degree of a polynomial
287 .BI lsolve( equation-list ", " symbol-list )
288 \- solve system of linear equations
290 .BI nops( expression )
291 \- number of operands in expression
293 .BI normal( "expression [" ", " level] )
294 \- rational function normalization
296 .BI numer( expression )
297 \- numerator of a rational function
299 .BI op( expression ", " number )
300 \- extract operand from expression
302 .BI power( expr1 ", " expr2 )
303 \- exponentiation (equivalent to writing expr1^expr2)
305 .BI prem( expression ", " expression ", " symbol )
306 \- pseudo-remainder of polynomials
308 .BI primpart( expression ", " symbol )
309 \- primitive part of a polynomial
311 .BI quo( expression ", " expression ", " symbol )
312 \- quotient of polynomials
314 .BI rem( expression ", " expression ", " symbol )
315 \- remainder of polynomials
317 .BI series( expression ", " relation-or-symbol ", " order )
320 .BI sqrfree( expression ", " symbol )
321 \- square-free factorization of a polynomial
323 .BI sqrt( expression )
326 .BI subs( expression ", " relation-or-list )
328 .BI subs( expression ", " look-for-list ", " replace-by-list )
329 \- substitute subexpressions
331 .BI tcoeff( expression ", " symbol )
332 \- trailing coefficient of a polynomial
334 .BI time( expression )
335 \- returns the time in seconds needed to evaluate the given expression
340 .BI transpose( matrix )
341 \- transpose of a matrix
343 .BI unassign( symbol )
344 \- unassign an assigned symbol
346 .BI unit( expression ", " symbol )
347 \- unit part of a polynomial
349 \" GINSH_FCN_HELP_END
361 ginsh can display a (short) help for a given topic (mostly about functions
362 and operators) by entering
370 will display a list of available help topics.
374 .BI print( expression );
376 will print a dump of GiNaC's internal representation for the given
378 This is useful for debugging and for learning about GiNaC internals.
382 .BI iprint( expression );
386 (which must evaluate to an integer) in decimal, octal, and hexadecimal representations.
388 Finally, the shell escape
391 .RI [ "command " [ arguments ]]
397 to the shell for execution. With this method, you can execute shell commands
398 from within ginsh without having to quit.
406 (x+1)^(\-2)*(\-x+x^2\-2)
408 (2*x\-1)*(x+1)^(\-2)\-2*(x+1)^(\-3)*(\-x+x^2\-2)
412 717897987691852588770249
414 717897987691852588770247/717897987691852588770250
418 0.999999999999999999999995821133292704384960990679L0
422 (x+1)^(\-2)*(\-x+x^2\-2)
423 > lsolve([3*x+5*y == 7], [x, y]);
424 [x==\-5/3*y+7/3,y==y]
425 > lsolve([3*x+5*y == 7, \-2*x+10*y == \-5], [x, y]);
427 > M = [[ [[a, b]], [[c, d]] ]];
428 [[ [[\-x+x^2\-2,(x+1)^2]], [[c,d]] ]]
430 \-2*d\-2*x*c\-x^2*c\-x*d+x^2*d\-c
432 (\-d\-2*c)*x+(d\-c)*x^2\-2*d\-c
433 > solve quantum field theory;
434 parse error at quantum
439 .RI "parse error at " foo
440 You entered something which ginsh was unable to parse. Please check the syntax
441 of your input and try again.
443 .RI "argument " num " to " function " must be a " type
448 must be of a certain type (e.g. a symbol, or a list). The first argument has
449 number 0, the second argument number 1, etc.
454 Christian Bauer <Christian.Bauer@uni-mainz.de>
456 Alexander Frink <Alexander.Frink@uni-mainz.de>
458 Richard Kreckel <Richard.Kreckel@uni-mainz.de>
460 GiNaC Tutorial \- An open framework for symbolic computation within the
461 C++ programming language
463 CLN \- A Class Library for Numbers, Bruno Haible
465 Copyright \(co 1999-2000 Johannes Gutenberg Universit\(:at Mainz, Germany
467 This program is free software; you can redistribute it and/or modify
468 it under the terms of the GNU General Public License as published by
469 the Free Software Foundation; either version 2 of the License, or
470 (at your option) any later version.
472 This program is distributed in the hope that it will be useful,
473 but WITHOUT ANY WARRANTY; without even the implied warranty of
474 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
475 GNU General Public License for more details.
477 You should have received a copy of the GNU General Public License
478 along with this program; if not, write to the Free Software
479 Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.