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radexpand-sqrt

a:1/2*sqrt(2-sqrt(2+s...

radexpand:all;

b:sqrt((1-sqrt(1-a^2)...

Calculate

radexpand-sqrt-true

radexpand:true;

sqrt(x)*sqrt(x);

Calculate

radexpand-sqrt-true

radexpand:true;

(6+sqrt(52))/8;

Calculate

radexpand-sqrt-true

radexpand:true;

sqrt(120);

Calculate

radexpand

? radexpand;

Calculate

radexpand-sqrt

a:1/2*sqrt(2-sqrt(2+s...

radexpand:all;

b:sqrt((1-sqrt(1-a^2)...

Calculate

radexpand-sqrt-true

radexpand:true;

sqrt(x)*sqrt(x);

Calculate

radexpand-sqrt-true

radexpand:true;

(6+sqrt(52))/8;

Calculate

radexpand-sqrt-true

radexpand:true;

sqrt(120);

Calculate

radexpand

? radexpand;

Calculate

radexpand

Run Example
(%i1)simp:false;
(%o1)                                false
(%i2) radexpand:false;
(%o2)                                false
(%i3) 1/a, simp:false;
                                       1
(%o3)                                  -
                                       a
(%i4) 1/b, simp:false;
                                       1
(%o4)                                  -
                                       b
(%i5) 1/(a*b), simp:false;
                                       1
(%o5)                                 ---
                                      a b
(%i6) tellsimp(1/(a*b), ((1/a)*(1/b)));
(%o6)                         [/rule1, simpquot]
(%i7) 1/(a*b);
                                       1
(%o7)                                 ---
                                      a b
(%i8) disprule(all);
                                       1     1  1
(%t8)                        /rule1 : --- -> - (-)
                                      a b    a  b

(%o8)                                [%t8]
(%i9) 1/(a*b);
                                       1
(%o9)                                 ---
                                      a b
(%i10) properties("*");
(%o10)              [mirror symmetry, nary, rule, operator]
(%i11) rat(1/(a*b));
                                       1
(%o11)/R/                             ---
                                      a b
(%i12) map('ratsimp, 1/(a*b));
                                       1
(%o12)                                ---
                                      a b
(%i13) grind(1/(a*b));

1/(a*b)$
(%o13)                               done
(%i14) partfrac(1/(a*b), a);
                                     1  - 1
(%o14)                            + (- a   )
                                     b
(%i15) a^-1;
                                      - 1
(%o15)                               a
(%i16) 
Run Example
2/(1-2);
(%o1)                                 - 2
(%i2) 3/(1-3);
                                        3
(%o2)                                 - -
                                        2
(%i3) 4/(1-4);
                                        4
(%o3)                                 - -
                                        3
(%i4) 5/(1-5);
                                        5
(%o4)                                 - -
                                        4
(%i5) 6/(1-6);
                                        6
(%o5)                                 - -
                                        5
(%i6) x/(1-x);
                                       x
(%o6)                                -----
                                     1 - x
(%i7) (x/(1-x)), simplify;
                                       x
(%o7)                                -----
                                     1 - x
(%i8) (x/(1-x)), factor;
                                        x
(%o8)                               - -----
                                      x - 1
(%i9) (x/(1-x)), expand;
                                       x
(%o9)                                -----
                                     1 - x
(%i10) (x/(1-x)), radcan;
                                        x
(%o10)                              - -----
                                      x - 1
(%i11) (2/(1-2*x) - 1/(1-x));
                                   2        1
(%o11)                          ------- - -----
                                1 - 2 x   1 - x
(%i12) (2/(1-2*x) - 1/(1-x)), expand;
                                   2        1
(%o12)                          ------- - -----
                                1 - 2 x   1 - x
(%i13) (2/(1-2*x) - 1/(1-x)), radexpand;
                                   2        1
(%o13)                          ------- - -----
                                1 - 2 x   1 - x
(%i14) (2/(1-2*x) - 1/(1-x)), factor;
                                       1
(%o14)                         -----------------
                               (x - 1) (2 x - 1)
(%i15) (2/(1-2*x) - 1/(1-x)), radcan;
                                      1
(%o15)                          --------------
                                   2
                                2 x  - 3 x + 1
(%i16) x*(2/(1-2*x) - 1/(1-x)), factor;
                                       x
(%o16)                         -----------------
                               (x - 1) (2 x - 1)
(%i17) x*(2/(1-2*x) - 1/(1-x)), radcan;
                                      x
(%o17)                          --------------
                                   2
                                2 x  - 3 x + 1
(%i18) x*(2/(1-2*x) - 1/(1-x)), expand;
                                  2 x       x
(%o18)                          ------- - -----
                                1 - 2 x   1 - x
(%i19) x*(2/(1-2*x) - 1/(1-x)), radexpand;
                                  2        1
(%o19)                        (------- - -----) x
                               1 - 2 x   1 - x
(%i20) x*(2/(1-2*x) - 1/(1-x)), simplify;
                                  2        1
(%o20)                        (------- - -----) x
                               1 - 2 x   1 - x
(%i21) y : (2/(1-2*x) - 1/(1-x)),radcan;
                                      1
(%o21)                          --------------
                                   2
                                2 x  - 3 x + 1
(%i22) sum(y, y, 1, 3);
(%o22)                                 6
(%i23) sumcontract(y);
                                      1
(%o23)                          --------------
                                   2
                                2 x  - 3 x + 1
(%i24) taylor(y);
                                  1
(%o24)/T/                   -------------- + . . .
                               2
                            2 x  - 3 x + 1
(%i25) taylor(x*y);
                                  x
(%o25)/T/                   -------------- + . . .
                               2
                            2 x  - 3 x + 1
(%i26) taylor(x*y), radcan;
                                      x
(%o26)                          --------------
                                   2
                                2 x  - 3 x + 1
(%i27) 
Run Example
? radexpand;

 -- Option variable: radexpand
     Default value: `true'

     `radexpand' controls some simplifications of radicals.

     When `radexpand' is `all', causes nth roots of factors of a
     product which are powers of n to be pulled outside of the radical.
     E.g. if `radexpand' is `all', `sqrt (16*x^2)' simplifies to `4*x'.

     More particularly, consider `sqrt (x^2)'.
        * If `radexpand' is `all' or `assume (x > 0)' has been executed,
          `sqrt(x^2)' simplifies to `x'.

        * If `radexpand' is `true' and `domain' is `real' (its default),
          `sqrt(x^2)' simplifies to `abs(x)'.

        * If `radexpand' is `false', or `radexpand' is `true' and
          `domain' is `complex', `sqrt(x^2)' is not simplified.

     Note that `domain' only matters when `radexpand' is `true'.


(%o1)                                true
(%i2) 

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