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 curly brace
196 a (possibly empty) comma-separated sequence of expressions, and a closing curly
200 A matrix consists of an opening square bracket
202 a non-empty comma-separated sequence of matrix rows, and a closing square bracket
204 Each matrix row consists of an opening square bracket
206 a non-empty comma-separated sequence of expressions, and a closing square bracket
208 If the rows of a matrix are not of the same length, the width of the matrix
209 becomes that of the longest row and shorter rows are filled up at the end
210 with elements of value zero.
212 A function call in ginsh has the form
214 .IB name ( arguments )
218 is a comma-separated sequence of expressions. ginsh provides a couple of built-in
219 functions and also "imports" all symbolic functions defined by GiNaC and additional
220 libraries. There is no way to define your own functions other than linking ginsh
221 against a library that defines symbolic GiNaC functions.
223 ginsh provides Tab-completion on function names: if you type the first part of
224 a function name, hitting Tab will complete the name if possible. If the part you
225 typed is not unique, hitting Tab again will display a list of matching functions.
226 Hitting Tab twice at the prompt will display the list of all available functions.
228 A list of the built-in functions follows. They nearly all work as the
229 respective GiNaC methods of the same name, so I will not describe them in
230 detail here. Please refer to the GiNaC documentation.
233 \" GINSH_FCN_HELP_START
234 .BI charpoly( matrix ", " symbol )
235 \- characteristic polynomial of a matrix
237 .BI coeff( expression ", " object ", " number )
238 \- extracts coefficient of object^number from a polynomial
240 .BI collect( expression ", " object-or-list )
241 \- collects coefficients of like powers (result in recursive form)
243 .BI collect_distributed( expression ", " list )
244 \- collects coefficients of like powers (result in distributed form)
246 .BI content( expression ", " symbol )
247 \- content part of a polynomial
249 .BI decomp_rational( expression ", " symbol )
250 \- decompose rational function into polynomial and proper rational function
252 .BI degree( expression ", " object )
253 \- degree of a polynomial
255 .BI denom( expression )
256 \- denominator of a rational function
258 .BI determinant( matrix )
259 \- determinant of a matrix
261 .BI diag( expression... )
262 \- constructs diagonal matrix
264 .BI diff( expression ", " "symbol [" ", " number] )
265 \- partial differentiation
267 .BI divide( expression ", " expression )
268 \- exact polynomial division
270 .BI eval( "expression [" ", " level] )
271 \- evaluates an expression, replacing symbols by their assigned value
273 .BI evalf( "expression [" ", " level] )
274 \- evaluates an expression to a floating point number
276 .BI evalm( expression )
277 \- evaluates sums, products and integer powers of matrices
279 .BI expand( expression )
280 \- expands an expression
282 .BI gcd( expression ", " expression )
283 \- greatest common divisor
285 .BI has( expression ", " expression )
286 \- returns "1" if the first expression contains the second (which may contain wildcards) as a subexpression, "0" otherwise
288 .BI inverse( matrix )
289 \- inverse of a matrix
292 \- returns "1" if the relation is true, "0" otherwise (false or undecided)
294 .BI lcm( expression ", " expression )
295 \- least common multiple
297 .BI lcoeff( expression ", " object )
298 \- leading coefficient of a polynomial
300 .BI ldegree( expression ", " object )
301 \- low degree of a polynomial
303 .BI lsolve( equation-list ", " symbol-list )
304 \- solve system of linear equations
306 .BI match( expression ", " pattern )
307 \- check whether expression matches a pattern; returns a list of wildcard substitutions or "FAIL" if there is no match
309 .BI nops( expression )
310 \- number of operands in expression
312 .BI normal( "expression [" ", " level] )
313 \- rational function normalization
315 .BI numer( expression )
316 \- numerator of a rational function
318 .BI numer_denom( expression )
319 \- numerator and denumerator of a rational function as a list
321 .BI op( expression ", " number )
322 \- extract operand from expression
324 .BI power( expr1 ", " expr2 )
325 \- exponentiation (equivalent to writing expr1^expr2)
327 .BI prem( expression ", " expression ", " symbol )
328 \- pseudo-remainder of polynomials
330 .BI primpart( expression ", " symbol )
331 \- primitive part of a polynomial
333 .BI quo( expression ", " expression ", " symbol )
334 \- quotient of polynomials
336 .BI rem( expression ", " expression ", " symbol )
337 \- remainder of polynomials
339 .BI series( expression ", " relation-or-symbol ", " order )
342 .BI sqrfree( "expression [" ", " symbol-list] )
343 \- square-free factorization of a polynomial
345 .BI sqrt( expression )
348 .BI subs( expression ", " relation-or-list )
350 .BI subs( expression ", " look-for-list ", " replace-by-list )
351 \- substitute subexpressions (you may use wildcards)
353 .BI tcoeff( expression ", " object )
354 \- trailing coefficient of a polynomial
356 .BI time( expression )
357 \- returns the time in seconds needed to evaluate the given expression
362 .BI transpose( matrix )
363 \- transpose of a matrix
365 .BI unassign( symbol )
366 \- unassign an assigned symbol
368 .BI unit( expression ", " symbol )
369 \- unit part of a polynomial
371 \" GINSH_FCN_HELP_END
383 ginsh can display a (short) help for a given topic (mostly about functions
384 and operators) by entering
392 will display a list of available help topics.
396 .BI print( expression );
398 will print a dump of GiNaC's internal representation for the given
400 This is useful for debugging and for learning about GiNaC internals.
404 .BI iprint( expression );
408 (which must evaluate to an integer) in decimal, octal, and hexadecimal representations.
410 Finally, the shell escape
413 .RI [ "command " [ arguments ]]
419 to the shell for execution. With this method, you can execute shell commands
420 from within ginsh without having to quit.
428 (x+1)^(\-2)*(\-2\-x+x^2)
430 (2*x\-1)*(x+1)^(\-2)\-2*(x+1)^(\-3)*(\-x+x^2\-2)
434 717897987691852588770249
436 717897987691852588770247/717897987691852588770250
440 0.999999999999999999999995821133292704384960990679
444 (x+1)^(\-2)*(\-x+x^2\-2)
445 > series(sin(x),x==0,6);
446 1*x+(\-1/6)*x^3+1/120*x^5+Order(x^6)
447 > lsolve({3*x+5*y == 7}, {x, y});
448 {x==\-5/3*y+7/3,y==y}
449 > lsolve({3*x+5*y == 7, \-2*x+10*y == \-5}, {x, y});
451 > M = [ [a, b], [c, d] ];
452 [[\-x+x^2\-2,(x+1)^2],[c,d]]
454 \-2*d\-2*x*c\-x^2*c\-x*d+x^2*d\-c
456 (\-d\-2*c)*x+(d\-c)*x^2\-2*d\-c
457 > solve quantum field theory;
458 parse error at quantum
463 .RI "parse error at " foo
464 You entered something which ginsh was unable to parse. Please check the syntax
465 of your input and try again.
467 .RI "argument " num " to " function " must be a " type
472 must be of a certain type (e.g. a symbol, or a list). The first argument has
473 number 0, the second argument number 1, etc.
478 Christian Bauer <Christian.Bauer@uni-mainz.de>
480 Alexander Frink <Alexander.Frink@uni-mainz.de>
482 Richard Kreckel <Richard.Kreckel@uni-mainz.de>
484 GiNaC Tutorial \- An open framework for symbolic computation within the
485 C++ programming language
487 CLN \- A Class Library for Numbers, Bruno Haible
489 Copyright \(co 1999-2001 Johannes Gutenberg Universit\(:at Mainz, Germany
491 This program is free software; you can redistribute it and/or modify
492 it under the terms of the GNU General Public License as published by
493 the Free Software Foundation; either version 2 of the License, or
494 (at your option) any later version.
496 This program is distributed in the hope that it will be useful,
497 but WITHOUT ANY WARRANTY; without even the implied warranty of
498 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
499 GNU General Public License for more details.
501 You should have received a copy of the GNU General Public License
502 along with this program; if not, write to the Free Software
503 Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.