Re: Symbolic equation solving

[Sergei Steshenko]

----- Original Message -----
> From: Sergei Steshenko <address@hidden>
> To: Martin Helm <address@hidden>; vkv <address@hidden>
> Cc: "address@hidden" <address@hidden>
> Sent: Friday, June 8, 2012 3:54 PM
> Subject: Re: Symbolic equation solving
> 
> 
> 
> 
> 
> ----- Original Message -----
>>  From: Martin Helm <address@hidden>
>>  To: vkv <address@hidden>
>>  Cc: address@hidden
>>  Sent: Friday, June 8, 2012 12:26 PM
>>  Subject: Re: Symbolic equation solving
>> 
>> T he symbolic package is partially broken at the moment, that does not
>>  say that this is the reason for your problem or something else.
>>  It needs volunteers to support it.
>>  The workaround is to use one of the free computer algebra systems out
>>  there like maxima, sage, sympy, the free version of axiom ...
>>  _______________________________________________
> 
> 
> There is also Mathomatic: http://www.mathomatic.org/math/ . And one can try 
> it 
> in his/her web browser: http://mathomatic.orgserve.de/CGI/math.php .
> 
> And it is easy to build because of no dependencies (or a dependency on GNU 
> 'readline').
> 
> But it's probably not as powerful as mentioned above packages.
> 
> Regards,
>   Sergei.
> 


And, by the way, the symbolic package is based on GiNaC: http://www.ginac.de/ .

Which has an interactive shell. After barely RTFMing I'm able to produce the 
following:


"
address@hidden:~/junk> 
/mnt/sdb8/sergei/AFSWD_debug/20120424/ginac-1.6.2/binsh/ginsh
ginsh - GiNaC Interactive Shell (ginac V1.6.2)
  __,  _______  Copyright (C) 1999-2011 Johannes Gutenberg University Mainz,
 (__) *       | Germany.  This is free software with ABSOLUTELY NO WARRANTY.
  ._) i N a C | You are welcome to redistribute it under certain conditions.
<-------------' For details type `warranty;'.

Type ?? for a list of help topics.
> foo = a*b + a*c;
a*b+c*a
> factor(foo);
(c+b)*a
>
".

FTM:

"
              charpoly(matrix, symbol) - characteristic polynomial of a matrix
              coeff(expression, object, number) - extracts coefficient of 
object^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
              eval(expression [, level]) - evaluates an expression, replacing 
symbols by their assigned value
              evalf(expression [, level]) - evaluates an expression to a 
floating point number
              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 
contains 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 
equations
              map(expression, pattern) - apply function to each operand; the 
function to be applied is specified as a pattern with the "$0" wildcard 
standing for the operands
              match(expression, pattern) - check whether expression matches a 
pattern; returns a list of wildcard substitutions or "FAIL" if there is no match
              nops(expression) - number of operands in expression
              normal(expression [, level]) - 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 
polynomials
              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 
polynomials with respect to symbol s
              series(expression, relation-or-symbol, order) - series expansion
              sprem(expression, expression, symbol) - sparse pseudo-remainder 
of polynomials
              sqrfree(expression [, symbol-list]) - square-free factorization 
of a polynomial
              sqrt(expression) - square root
              subs(expression, relation-or-list)
              subs(expression, look-for-list, replace-by-list) - substitute 
subexpressions (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
".

Regards,
  Sergei.