Maxima Manual: Package functs

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### 69.4 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);
      (%o2) matrix([f(x),g(x)],['diff(f(x),x,1),'diff(g(x),x,1)])

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 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")`.

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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