Fractional exponents vs. radical form ...

03102020, 09:40 AM
Post: #1




Fractional exponents vs. radical form ...
Pardon my English, but math is not my native language:
Frustration: Expressions, (or equations), similar to x^([even numbered numerator]/denominator), when x<0. An Example: (1)^(2/3); ==> (1/2)+i*sqrt(3)/2 (3) NTHROOT ((1)^2); ==> 1, the desired result f(x):=(x^(2/3)); g(x):=((3) NTHROOT (x^2)); subst({f(x), g(x)}, x=(1)); ==> {((1/2)+(i*sqrt(3)/2))^2,1} A setting would be nice, that would force fractional exponents, to be the same as their radical form ... not sure how to best define it, but like obscenity, "I know it when I see it!" Dale 

03102020, 02:46 PM
(This post was last modified: 03102020 03:06 PM by Albert Chan.)
Post: #2




RE: Fractional exponents vs. radical form ...
XCas> radpow(a,b) := surd(a^numer(b), denom(b))
numer(b), denom(b) had b simplified first, which is exactly what we wanted Note: this assumed b is not symbolic variable XCas> radpow(64, 2/6) // = radpow(64, 1/3) = surd(64,3) = 4 XCas> radpow(64, 3/6) // = radpow(64, 1/2) = surd(64,2) = 8*i XCas> radpow(64, 4/6) // = radpow(64, 2/3) = surd(4096,3) = 16 see https://www.math.ubc.ca/~israel/advisor/.../a37r1.htm 

03102020, 02:51 PM
Post: #3




RE: Fractional exponents vs. radical form ...
(03102020 09:40 AM)DrD Wrote: Pardon my English, but math is not my native language: The root function has a different defining area/range from rational or reciprocal exponent function. That according to high school math. 

03102020, 04:53 PM
Post: #4




RE: Fractional exponents vs. radical form ...
Aside from the pure mathematical rigor, a setting allowing the user this option looks useful.


03102020, 07:34 PM
Post: #5




RE: Fractional exponents vs. radical form ...  
03112020, 12:56 AM
Post: #6




RE: Fractional exponents vs. radical form ...
I agree that the decimal approximation would produce an answer of the sort that was objected to (or at least asked for a choice in how the fractional power was interpreted). A choice would be nice for a fractional exponent that could be interpreted as symbolically equivalent to a surf/nroot as an option.


03112020, 01:01 AM
Post: #7




RE: Fractional exponents vs. radical form ...
(03112020 12:56 AM)lrdheat Wrote: I agree that the decimal approximation would produce an answer of the sort that was objected to (or at least asked for a choice in how the fractional power was interpreted). A choice would be nice for a fractional exponent that could be interpreted as symbolically equivalent to a surf/nroot as an option. no 

03112020, 08:50 AM
Post: #8




RE: Fractional exponents vs. radical form ...
(03102020 02:51 PM)CyberAngel Wrote: The root function has a different defining area/range from rational or reciprocal exponent function. The use of parentheses, (1) in my original example, was an important distinction, (to clarify the order of operations). My thinking was that: x^[even numerator]/denominator; would result in a realvalue, regardless of the fractional vs. radical form, (for realvalue inputs). Example: x^(2/1) where x=(n) Processed as: [(n) * (n)] = (+)n^2, not: 1 * (n * n) = ()n^2. 

« Next Oldest  Next Newest »

User(s) browsing this thread: 1 Guest(s)