1 .TH ginsh 1 "January, 2000" "GiNaC @VERSION@" "The GiNaC Group"
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.
113 The has(), match() and subs() functions accept wildcards as placeholders for
114 expressions. These have the syntax
118 for example $0, $1 etc.
119 .SS LAST PRINTED EXPRESSIONS
120 ginsh provides the three special symbols
124 that refer to the last, second last, and third last printed expression, respectively.
125 These are handy if you want to use the results of previous computations in a new
128 ginsh provides the following operators, listed in falling order of precedence:
131 \" GINSH_OP_HELP_START
148 non-commutative multiplication
182 All binary operators are left-associative, with the exception of
184 which are right-associative. The result of the assignment operator
186 is its right-hand side, so it's possible to assign multiple symbols in one
188 .BR "a = b = c = 2;" ).
190 Lists are used by the
194 functions. A list consists of an opening square bracket
196 a (possibly empty) comma-separated sequence of expressions, and a closing square
200 A matrix consists of an opening double square bracket
202 a non-empty comma-separated sequence of matrix rows, and a closing double square
205 Each matrix row consists of an opening double square bracket
207 a non-empty comma-separated sequence of expressions, and a closing double square
210 If the rows of a matrix are not of the same length, the width of the matrix
211 becomes that of the longest row and shorter rows are filled up at the end
212 with elements of value zero.
214 A function call in ginsh has the form
216 .IB name ( arguments )
220 is a comma-separated sequence of expressions. ginsh provides a couple of built-in
221 functions and also "imports" all symbolic functions defined by GiNaC and additional
222 libraries. There is no way to define your own functions other than linking ginsh
223 against a library that defines symbolic GiNaC functions.
225 ginsh provides Tab-completion on function names: if you type the first part of
226 a function name, hitting Tab will complete the name if possible. If the part you
227 typed is not unique, hitting Tab again will display a list of matching functions.
228 Hitting Tab twice at the prompt will display the list of all available functions.
230 A list of the built-in functions follows. They nearly all work as the
231 respective GiNaC methods of the same name, so I will not describe them in
232 detail here. Please refer to the GiNaC documentation.
235 \" GINSH_FCN_HELP_START
236 .BI charpoly( matrix ", " symbol )
237 \- characteristic polynomial of a matrix
239 .BI coeff( expression ", " object ", " number )
240 \- extracts coefficient of object^number from a polynomial
242 .BI collect( expression ", " object-or-list )
243 \- collects coefficients of like powers (result in recursive form)
245 .BI collect_distributed( expression ", " list )
246 \- collects coefficients of like powers (result in distributed form)
248 .BI content( expression ", " symbol )
249 \- content part of a polynomial
251 .BI degree( expression ", " object )
252 \- degree of a polynomial
254 .BI denom( expression )
255 \- denominator of a rational function
257 .BI determinant( matrix )
258 \- determinant of a matrix
260 .BI diag( expression... )
261 \- constructs diagonal matrix
263 .BI diff( expression ", " "symbol [" ", " number] )
264 \- partial differentiation
266 .BI divide( expression ", " expression )
267 \- exact polynomial division
269 .BI eval( "expression [" ", " level] )
270 \- evaluates an expression, replacing symbols by their assigned value
272 .BI evalf( "expression [" ", " level] )
273 \- evaluates an expression to a floating point number
275 .BI expand( expression )
276 \- expands an expression
278 .BI gcd( expression ", " expression )
279 \- greatest common divisor
281 .BI has( expression ", " expression )
282 \- returns "1" if the first expression contains the second (which may contain wildcards) as a subexpression, "0" otherwise
284 .BI inverse( matrix )
285 \- inverse of a matrix
288 \- returns "1" if the relation is true, "0" otherwise (false or undecided)
290 .BI lcm( expression ", " expression )
291 \- least common multiple
293 .BI lcoeff( expression ", " object )
294 \- leading coefficient of a polynomial
296 .BI ldegree( expression ", " object )
297 \- low degree of a polynomial
299 .BI lsolve( equation-list ", " symbol-list )
300 \- solve system of linear equations
302 .BI match( expression ", " pattern )
303 \- check whether expression matches a pattern; returns a list of wildcard substitutions or "FAIL" if there is no match
305 .BI nops( expression )
306 \- number of operands in expression
308 .BI normal( "expression [" ", " level] )
309 \- rational function normalization
311 .BI numer( expression )
312 \- numerator of a rational function
314 .BI numer_denom( expression )
315 \- numerator and denumerator of a rational function as a list
317 .BI op( expression ", " number )
318 \- extract operand from expression
320 .BI power( expr1 ", " expr2 )
321 \- exponentiation (equivalent to writing expr1^expr2)
323 .BI prem( expression ", " expression ", " symbol )
324 \- pseudo-remainder of polynomials
326 .BI primpart( expression ", " symbol )
327 \- primitive part of a polynomial
329 .BI quo( expression ", " expression ", " symbol )
330 \- quotient of polynomials
332 .BI rem( expression ", " expression ", " symbol )
333 \- remainder of polynomials
335 .BI series( expression ", " relation-or-symbol ", " order )
338 .BI sqrfree( "expression [" ", " symbol-list] )
339 \- square-free factorization of a polynomial
341 .BI sqrt( expression )
344 .BI subs( expression ", " relation-or-list )
346 .BI subs( expression ", " look-for-list ", " replace-by-list )
347 \- substitute subexpressions (you may use wildcards)
349 .BI tcoeff( expression ", " object )
350 \- trailing coefficient of a polynomial
352 .BI time( expression )
353 \- returns the time in seconds needed to evaluate the given expression
358 .BI transpose( matrix )
359 \- transpose of a matrix
361 .BI unassign( symbol )
362 \- unassign an assigned symbol
364 .BI unit( expression ", " symbol )
365 \- unit part of a polynomial
367 \" GINSH_FCN_HELP_END
379 ginsh can display a (short) help for a given topic (mostly about functions
380 and operators) by entering
388 will display a list of available help topics.
392 .BI print( expression );
394 will print a dump of GiNaC's internal representation for the given
396 This is useful for debugging and for learning about GiNaC internals.
400 .BI iprint( expression );
404 (which must evaluate to an integer) in decimal, octal, and hexadecimal representations.
406 Finally, the shell escape
409 .RI [ "command " [ arguments ]]
415 to the shell for execution. With this method, you can execute shell commands
416 from within ginsh without having to quit.
424 (x+1)^(\-2)*(\-2\-x+x^2)
426 (2*x\-1)*(x+1)^(\-2)\-2*(x+1)^(\-3)*(\-x+x^2\-2)
430 717897987691852588770249
432 717897987691852588770247/717897987691852588770250
436 0.999999999999999999999995821133292704384960990679
440 (x+1)^(\-2)*(\-x+x^2\-2)
441 > series(sin(x),x==0,6);
442 1*x+(\-1/6)*x^3+1/120*x^5+Order(x^6)
443 > lsolve([3*x+5*y == 7], [x, y]);
444 [x==\-5/3*y+7/3,y==y]
445 > lsolve([3*x+5*y == 7, \-2*x+10*y == \-5], [x, y]);
447 > M = [[ [[a, b]], [[c, d]] ]];
448 [[ [[\-x+x^2\-2,(x+1)^2]], [[c,d]] ]]
450 \-2*d\-2*x*c\-x^2*c\-x*d+x^2*d\-c
452 (\-d\-2*c)*x+(d\-c)*x^2\-2*d\-c
453 > solve quantum field theory;
454 parse error at quantum
459 .RI "parse error at " foo
460 You entered something which ginsh was unable to parse. Please check the syntax
461 of your input and try again.
463 .RI "argument " num " to " function " must be a " type
468 must be of a certain type (e.g. a symbol, or a list). The first argument has
469 number 0, the second argument number 1, etc.
474 Christian Bauer <Christian.Bauer@uni-mainz.de>
476 Alexander Frink <Alexander.Frink@uni-mainz.de>
478 Richard Kreckel <Richard.Kreckel@uni-mainz.de>
480 GiNaC Tutorial \- An open framework for symbolic computation within the
481 C++ programming language
483 CLN \- A Class Library for Numbers, Bruno Haible
485 Copyright \(co 1999-2001 Johannes Gutenberg Universit\(:at Mainz, Germany
487 This program is free software; you can redistribute it and/or modify
488 it under the terms of the GNU General Public License as published by
489 the Free Software Foundation; either version 2 of the License, or
490 (at your option) any later version.
492 This program is distributed in the hope that it will be useful,
493 but WITHOUT ANY WARRANTY; without even the implied warranty of
494 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
495 GNU General Public License for more details.
497 You should have received a copy of the GNU General Public License
498 along with this program; if not, write to the Free Software
499 Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.