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RPN / ABS |
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ABS (Absolute Value: function, |x|)
x → |x|
(x,y) → sqrt(x^2+y^2)
x_unit → |x|_unit
[array] → ||array||
'symb' → 'ABS(symb)'
Keyboard Access:
| 48S: | |
| MTH PARTS ABS | |
| MTH VECTR ABS | |
| MTH MATR NXT ABS |
| 48G: | |
| MTH VECTR ABS | |
| MTH MATR NORM ABS | |
| MTH REAL NXT ABS | |
| MTH NXT CMPL ABS |
| 49G: | |
| keyboard (left-shift ÷) | |
| CMPLX ABS | |
| MATRICES OPER ABS | |
| MTH VECTR ABS | |
| MTH REAL NXT ABS | |
| MTH MATRX NORM ABS | |
| MTH NXT CMPLX ABS | |
| <<CMPLX>> ABS |
Inverse: none
LASTARG: 1
Integer limit: no limit
Distance from origin, calculated as the square root of the sum of the squares of all the number(s) in the input (with each complex number being taken as an ordered pair of reals). If n is how many numbers are in the input, then the input is a single point in n dimensions, and the output is how far it is from the origin (or, if you prefer, it's the magnitude of that vector, also known as its Frobenius Norm or Euclidean Norm). Automatic simplifications: 'ABS(X)' ABS --> 'ABS(X)'
'-X' ABS --> 'ABS(X)'
where X is any algebraic expression. Examples: How far is 5 from 0 on the number line?
5 ABS --> 5
because sqrt(5^2) = 5. How far is -5 from 0 on the number line?
-5 ABS --> 5
because sqrt((-5)^2) = 5. How far is 3+4i from the origin on the real/imaginary plane?
(3.,4.) ABS --> 5
because sqrt(3^2 + 4^2) = 5. Note: ABS can be used to force any unit to be positive:
-5_ml ABS --> 5_ml What is the Eucliden norm (aka Frobenius norm) of [1 2 3 4 5]?
[1 2 3 4 5] ABS --> sqrt(55)
because that's what sqrt(1^2 + 2^2 + 3^2 + 4^2 + 5^2) simplifies to.
Therefore the point (1,2,3,4,5) in a 5-dimensional system lies exactly sqrt(55) (approx 7.4162) units from the origin. How far is (1,5,7,11) from (0,0,0,0)?
[1 5 7 11] ABS --> 14 When the calculator is put into POLAR mode (either CYLIN or SPHERE mode), the ABS of all 2D and 3D vectors is automatically calculated and displayed. If you do a lot of vector math, consider keeping your calculator in POLAR mode. Example: I drive 5 miles east, then 2 miles north, then 3 miles east, and finally 8 miles north. How far am I from my starting point?
Method 1: [5. 2.] [3. 8.] + ABS --> 12.8 miles
Method 2: (5 2) (3 8) + --> 12.8 (in POLAR mode) Related flags: -3 Related commands:
ARG? CYLIN? SPHERE?
BYTES: 2.5
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Page last modified on October 02, 2003, at 04:02 PM