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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")
.
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 ]
Returns the trace (sum of the diagonal elements) of matrix M.
To use this function write first load("functs")
.
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")
.
Returns true
if expr is nonzero and freeof (x, expr)
returns true
.
Returns false
otherwise.
To use this function write first load("functs")
.
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
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
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")
.
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")
.
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")
.
Returns the sum of the arithmetic series from 1 to n.
To use this function write first load("functs")
.
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")
.
Returns the Gaussian probability function
%e^(-x^2/2) / sqrt(2*%pi)
.
To use this function write first load("functs")
.
Returns the Gudermannian function
2*atan(%e^x)-%pi/2
.
To use this function write first load("functs")
.
Returns the inverse Gudermannian function
log (tan (%pi/4 + x/2))
.
To use this function write first load("functs")
.
Returns the versed sine 1 - cos (x)
.
To use this function write first load("functs")
.
Returns the coversed sine 1 - sin (x)
.
To use this function write first load("functs")
.
Returns the exsecant sec (x) - 1
.
To use this function write first load("functs")
.
Returns the haversine (1 - cos(x))/2
.
To use this function write first load("functs")
.
Returns the number of combinations of n objects taken r at a time.
To use this function write first load("functs")
.
Returns the number of permutations of r objects selected from a set of n objects.
To use this function write first load("functs")
.
Next: Package ineq, Previous: Package facexp, Up: simplification [Contents][Index]