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Rootscontract

Function: rootscontract (<expr>) Converts products of roots into roots of products. For example, rootscontract (sqrt(x)*y^(3/2)) yields sqrt(x*y^3).

When radexpand is true and domain is real, rootscontract converts abs into sqrt, e.g., rootscontract (abs(x)*sqrt(y)) yields sqrt(x^2*y).

There is an option rootsconmode affecting rootscontract as follows:

Problem Value of Result of applying rootsconmode rootscontract

x^(1/2)*y^(3/2) false (x*y^3)^(1/2) x^(1/2)*y^(1/4) false x^(1/2)*y^(1/4) x^(1/2)*y^(1/4) true (x*y^(1/2))^(1/2) x^(1/2)*y^(1/3) true x^(1/2)*y^(1/3) x^(1/2)*y^(1/4) all (x^2*y)^(1/4) x^(1/2)*y^(1/3) all (x^3*y^2)^(1/6)

When rootsconmode is false, rootscontract contracts only with respect to rational number exponents whose denominators are the same. The key to the rootsconmode: true examples is simply that 2 divides into 4 but not into 3. rootsconmode: all involves taking the least common multiple of the denominators of the exponents.

rootscontract uses ratsimp in a manner similar to logcontract.

Examples:

          (%i1) rootsconmode: false$
          (%i2) rootscontract (x^(1/2)*y^(3/2));
                                             3
          (%o2)                      sqrt(x y )
          (%i3) rootscontract (x^(1/2)*y^(1/4));
                                             1/4
          (%o3)                     sqrt(x) y
          (%i4) rootsconmode: true$
          (%i5) rootscontract (x^(1/2)*y^(1/4));
          (%o5)                    sqrt(x sqrt(y))
          (%i6) rootscontract (x^(1/2)*y^(1/3));
                                             1/3
          (%o6)                     sqrt(x) y
          (%i7) rootsconmode: all$
          (%i8) rootscontract (x^(1/2)*y^(1/4));
                                        2   1/4
          (%o8)                       (x  y)
          (%i9) rootscontract (x^(1/2)*y^(1/3));
                                       3  2 1/6
          (%o9)                      (x  y )
          (%i10) rootsconmode: false$
          (%i11) rootscontract (sqrt(sqrt(x) + sqrt(1 + x))
                              *sqrt(sqrt(1 + x) - sqrt(x)));
          (%o11)                          1
          (%i12) rootsconmode: true$
          (%i13) rootscontract (sqrt(5+sqrt(5)) - 5^(1/4)*sqrt(1+sqrt(5)));
          (%o13)                          0

(%o1)                                true
(%i2)