What is the meaning of 'simplify(n./d)?

What is the meaning of 'simplify(n./d)? I feel n./d is weird.

syms x

A=[3/2 (x^2+3)/(2*x-1)+3*x/(x-1);4/x^2,3*x+4]

pretty(simplify(A))

pretty(simplify(n./d)

[madhan ravi]

What's n and d?

[zhenyu zeng]

Yes, that is my question.

[madhan ravi]

You would get an error if n and d are not defined.

[zhenyu zeng]

No errors at all. It will get an answer.

[madhan ravi]

This is what I get:

>> syms x
   A=[3/2 (x^2+3)/(2*x-1)+3*x/(x-1);4/x^2,3*x+4]
   pretty(simplify(A))
   pretty(simplify(n./d)
 
A =
 
[   3/2, (3*x)/(x - 1) + (x^2 + 3)/(2*x - 1)]
[ 4/x^2,                             3*x + 4]
 
/               2     \
|  3   3 x     x  + 3 |
|  -, ----- + ------- |
|  2  x - 1   2 x - 1 |
|                     |
|  4                  |
| --,     3 x + 4     |
|  2                  |
\ x                   /

 pretty(simplify(n./d)
                      ↑
Error: Invalid expression. When calling a function or indexing a
variable, use parentheses. Otherwise, check for mismatched
delimiters.
 
Did you mean:
>> pretty(simplify(n./d))
Undefined function or variable 'n'.
 
>> 

[zhenyu zeng]

>> pretty(simplify(n./d))

/ 3 2 \

| 3 x + 5 x - 3 |

| -, ----------------- |

| 2 (2 x - 1) (x - 1) |

| |

| 4 |

| --, 3 x + 4 |

| 2 |

\ x /

R2018b

[madhan ravi]

Type

n
d

in command window and paste the results

[zhenyu zeng]

>> syms x

>> A=[3/2,(x^2+3)/(2*x-1)+3*x/(x-1);4/x^2,3*x+4]

A =

[ 3/2, (3*x)/(x - 1) + (x^2 + 3)/(2*x - 1)]

[ 4/x^2, 3*x + 4]

>> [n,d]=numden(A)

n =

[ 3, x^3 + 5*x^2 - 3]

[ 4, 3*x + 4]

d =

[ 2, (2*x - 1)*(x - 1)]

[ x^2, 1]

>> simplify(A)

ans =

[ 3/2, (3*x)/(x - 1) + (x^2 + 3)/(2*x - 1)]

[ 4/x^2, 3*x + 4]

>> pretty(simplify(n./d))

/ 3 2 \

| 3 x + 5 x - 3 |

| -, ----------------- |

| 2 (2 x - 1) (x - 1) |

| |

| 4 |

| --, 3 x + 4 |

| 2 |

\ x /

[Star Strider]

syms x 
n = ... 
[ 3, x^3 + 5*x^2 - 3;
 4,         3*x + 4];
 
 
d = ...
[   2, (2*x - 1)*(x - 1);
 x^2,                 1];

simplified_fraction = simplify(n/d, 'Steps',20) 

produces:

simplified_fraction =
[ -(- x^5 - 5*x^4 + 3*x^2 + 3)/(2*x^4 - 3*x^3 + x^2 - 2), -(2*x^3 + 4*x^2 + 9*x - 9)/(2*x^4 - 3*x^3 + x^2 - 2)]
[          (3*x^3 + 4*x^2 - 4)/(2*x^4 - 3*x^3 + x^2 - 2),   -(2*(- 4*x^2 + 9*x + 2))/(2*x^4 - 3*x^3 + x^2 - 2)]

Answer 1

[Steven Lord]

The expression n./d divides each element of n by the corresponding element of d (with a few caveats to that if they're different sizes.) Since in your example n and d are both sym objects, the result of n./d is also a sym object.

Calling simplify on a sym object attempts to simplify the symbolic expression. In this case, since n and d were created by a call to numden (which extracts the numerator and denominator of a symbolic expression) on the sym object A, n./d should be equivalent to A. If it isn't displayed the same as A initially, simplifying it may make the similarity more pronounced. If you want to check that they're always equal:

isAlways(A == n./d)

[zhenyu zeng]

What is the difference between n./d and n/d?

[Steven Lord]

Array operations versus matrix operations.