Nächste: Package ineq, Vorige: Package facexp, Nach oben: simplification [Inhalt][Index]
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); (%o2) matrix([f(x),g(x)],['diff(f(x),x,1),'diff(g(x),x,1)])
Returns the trace (sum of the diagonal elements) of matrix M.
To use this function write first load("functs")
.
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")
.
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 linear in variable x, linear
returns a*x + b
where a is nonzero,
and a and b are free of x.
Otherwise, linear
returns expr.
To use this function write first load("functs")
.
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")
.
Nächste: Package ineq, Vorige: Package facexp, Nach oben: simplification [Inhalt][Index]