(maxima.info)Package functs
81.4 Package functs
===================
-- Function: rempart (<expr>, <n>)
Removes part <n> from the expression <expr>.
If <n> is a list of the form '[<l>, <m>]' then parts <l> thru <m>
are removed.
To use this function write first 'load(functs)'.
-- Function: wronskian ([<f_1>, ..., <f_n>], <x>)
Returns the Wronskian matrix of the list of expressions [<f_1>,
..., <f_n>] in the variable <x>. The determinant of the Wronskian
matrix is the Wronskian determinant of the list of expressions.
To use 'wronskian', first 'load(functs)'. Example:
(%i1) load ("functs")$
(%i2) wronskian([f(x), g(x)],x);
[ f(x) g(x) ]
[ ]
(%o2) [ d d ]
[ -- (f(x)) -- (g(x)) ]
[ dx dx ]
-- Function: tracematrix (<M>)
Returns the trace (sum of the diagonal elements) of matrix <M>.
To use this function write first 'load(functs)'.
-- Function: rational (<z>)
Multiplies numerator and denominator of <z> by the complex
conjugate of denominator, thus rationalizing the denominator.
Returns canonical rational expression (CRE) form if given one, else
returns general form.
To use this function write first 'load(functs)'.
-- Function: nonzeroandfreeof (<x>, <expr>)
Returns 'true' if <expr> is nonzero and 'freeof (<x>, <expr>)'
returns 'true'. Returns 'false' otherwise.
To use this function write first 'load(functs)'.
-- Function: linear (<expr>, <x>)
When <expr> is an expression of the form '<a>*<x> + <b>' where <a>
is nonzero, and <a> and <b> are free of <x>, 'linear' returns a
list of three equations, one for each of the three formal variables
<b>, <a>, and <x>. Otherwise, 'linear' returns 'false'.
'load(antid)' loads this function.
Example:
(%i1) load ("antid");
(%o1) /maxima/share/integration/antid.mac
(%i2) linear ((1 - w)*(1 - x)*z, z);
(%o2) [bargumentb = 0, aargumenta = (w - 1) x - w + 1,
xargumentx = z]
(%i3) linear (cos(u - v) + cos(u + v), u);
(%o3) false
-- Function: gcdivide (<p>, <q>)
When the option variable 'takegcd' is 'true' which is the default,
'gcdivide' divides the polynomials <p> and <q> by their greatest
common divisor and returns the ratio of the results. 'gcdivde'
calls the function 'ezgcd' to divide the polynomials by the
greatest common divisor.
When 'takegcd' is 'false', 'gcdivide' returns the ratio '<p>/<q>'.
To use this function write first 'load(functs)'.
See also 'ezgcd', 'gcd', 'gcdex', and 'poly_gcd'.
Example:
(%i1) load(functs)$
(%i2) p1:6*x^3+19*x^2+19*x+6;
3 2
(%o2) 6 x + 19 x + 19 x + 6
(%i3) p2:6*x^5+13*x^4+12*x^3+13*x^2+6*x;
5 4 3 2
(%o3) 6 x + 13 x + 12 x + 13 x + 6 x
(%i4) gcdivide(p1, p2);
x + 1
(%o4) ------
3
x + x
(%i5) takegcd:false;
(%o5) false
(%i6) gcdivide(p1, p2);
3 2
6 x + 19 x + 19 x + 6
(%o6) ----------------------------------
5 4 3 2
6 x + 13 x + 12 x + 13 x + 6 x
(%i7) ratsimp(%);
x + 1
(%o7) ------
3
x + x
-- Function: arithmetic (<a>, <d>, <n>)
Returns the <n>-th term of the arithmetic series '<a>, <a> + <d>,
<a> + 2*<d>, ..., <a> + (<n> - 1)*<d>'.
To use this function write first 'load(functs)'.
-- Function: geometric (<a>, <r>, <n>)
Returns the <n>-th term of the geometric series '<a>, <a>*<r>,
<a>*<r>^2, ..., <a>*<r>^(<n> - 1)'.
To use this function write first 'load(functs)'.
-- Function: harmonic (<a>, <b>, <c>, <n>)
Returns the <n>-th term of the harmonic series '<a>/<b>, <a>/(<b> +
<c>), <a>/(<b> + 2*<c>), ..., <a>/(<b> + (<n> - 1)*<c>)'.
To use this function write first 'load(functs)'.
-- Function: arithsum (<a>, <d>, <n>)
Returns the sum of the arithmetic series from 1 to <n>.
To use this function write first 'load(functs)'.
-- Function: geosum (<a>, <r>, <n>)
Returns the sum of the geometric series from 1 to <n>. If <n> is
infinity ('inf') then a sum is finite only if the absolute value of
<r> is less than 1.
To use this function write first 'load(functs)'.
-- Function: gaussprob (<x>)
Returns the Gaussian probability function '%e^(-<x>^2/2) /
sqrt(2*%pi)'.
To use this function write first 'load(functs)'.
-- Function: gd (<x>)
Returns the Gudermannian function '2*atan(%e^x)-%pi/2'.
To use this function write first 'load(functs)'.
-- Function: agd (<x>)
Returns the inverse Gudermannian function 'log (tan (%pi/4 +
x/2))'.
To use this function write first 'load(functs)'.
-- Function: vers (<x>)
Returns the versed sine '1 - cos (x)'.
To use this function write first 'load(functs)'.
-- Function: covers (<x>)
Returns the coversed sine '1 - sin (<x>)'.
To use this function write first 'load(functs)'.
-- Function: exsec (<x>)
Returns the exsecant 'sec (<x>) - 1'.
To use this function write first 'load(functs)'.
-- Function: hav (<x>)
Returns the haversine '(1 - cos(x))/2'.
To use this function write first 'load(functs)'.
-- Function: combination (<n>, <r>)
Returns the number of combinations of <n> objects taken <r> at a
time.
To use this function write first 'load(functs)'.
-- Function: permutation (<n>, <r>)
Returns the number of permutations of <r> objects selected from a
set of <n> objects.
To use this function write first 'load(functs)'.
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