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The Maxima on-line user's manual

Algebra Calculator

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Tellrat Calculator

Tellrat

Function: tellrat (<p_1>, ..., <p_n>)

load(functs);
polyfactor:true;
divide (expand(x^2-7*x+10),expand(x+3));
disp ((x^2-7*x-10)/(x+3));
gcdivide((x^2-7*x-10),(x+3));
tellrat ((x^2-7*x-10),(x+3));

Function: tellrat () Adds to the ring of algebraic integers known to Maxima the elements which are the solutions of the polynomials <p_1>, ..., <p_n>. Each argument <p_i> is a polynomial with integer coefficients.

tellrat (<x>) effectively means substitute 0 for <x> in rational functions.

tellrat () returns a list of the current substitutions.

algebraic must be set to true in order for the simplification of algebraic integers to take effect.

Maxima initially knows about the imaginary unit %i and all roots of integers.

There is a command untellrat which takes kernels and removes tellrat properties.

When tellrating a multivariate polynomial, e.g., tellrat (x^2 - y^2), there would be an ambiguity as to whether to substitute <y>^2 for <x>^2 or vice versa. Maxima picks a particular ordering, but if the user wants to specify which, e.g. tellrat (y^2 = x^2) provides a syntax which says replace <y>^2 by <x>^2.

Examples:

          (%i1) 10*(%i + 1)/(%i + 3^(1/3));
                                     10 (%i + 1)
          (%o1)                      -----------
                                            1/3
                                      %i + 3
          (%i2) ev (ratdisrep (rat(%)), algebraic);
                       2/3      1/3              2/3      1/3
          (%o2)    (4 3    - 2 3    - 4) %i + 2 3    + 4 3    - 2
          (%i3) tellrat (1 + a + a^2);
                                      2
          (%o3)                     [a  + a + 1]
          (%i4) 1/(a*sqrt(2) - 1) + a/(sqrt(3) + sqrt(2));
                                1                 a
          (%o4)           ------------- + -----------------
                          sqrt(2) a - 1   sqrt(3) + sqrt(2)
          (%i5) ev (ratdisrep (rat(%)), algebraic);
                   (7 sqrt(3) - 10 sqrt(2) + 2) a - 2 sqrt(2) - 1
          (%o5)    ----------------------------------------------
                                         7
          (%i6) tellrat (y^2 = x^2);
                                  2    2   2
          (%o6)                 [y  - x , a  + a + 1]

There are also some inexact matches for tellrat. Try ?? tellrat to see them.

(%o1)                                true
(%i2) 

Tellrat Example

Related Examples