MATLAB: Is this a symbolic math bug

Question

1. Let's a=log(2), I want create with only 5 digits:

>>digits(5);b=sym(a,'d')

b = 0.69315

But what is another way? This way isn't good while – by command digits I effect global changes — and I am forced to return: digits(32)

2. Perhaps one wants to include periodic ratio Suppose a working example: >> b=sym(0.69696969696969,'r') true result 69/99=23/33, but many signs are needed — on contrary: >> b=sym(0.6969,'r') b = 6969/10000

How to easy include, for example, 1.23(45) as ratio?

3. >> syms x positive;

>> x=solve('y=-1')

x = -1

But why was quiet reaction? How to clarify the attribute "positive" (in order to machine feel)?

4. And critical and scandal bug:

>> sym(0.6915 – 0.69,'d')

ans = 0.0015000000000000568434188608080149

at this: >>0.6915000-0.69

ans = 0.001500000000000

and also you may see:

>> sym(0.6915 – 0.69,'r')

ans = 211106232533/140737488355328

>> 211106232533/140737488355328

ans = 0.001500000000000

instead of sholar simple 15/10000

Answer 1

Thanks. To continue:

Q1 Solution based on your idea (oh.. I am stupid :)- ): >>a=log(2);a=sym(vpa(a,5))

Q2: to clarify -- notice for developer I want such reaction: >>a=sym('1.23(45)','r')

a= 679/550

MATLAB MUST tranform periodic kind of rational numbers in math: 1.234545454545..=1.23(45)=1.23+0.01*45/99=...=679/550

A valid script on this topic from another forum user (but I don't like it)

----

function numrat = forMatigor(numch)

% numch -> char ?????: numch = '1.23(45)'

I = regexp(numch,'[.(]');

J = length(numch)-1;

numrat = rats(eval([numch(1:I(2)-1) repmat( numch( I(2)+1:J),1,1+ceil((20-diff(I)+1)/(J-I(2))))]));

----

Also MATLAB would realize reverse: for example -- '1/3' -> '0.(3)'

Q3: yes, here is different (>>syms x positive):

solve('x=-1') VS solve('y=-1')

if both commands run without assigning to x -- it seems results are equavalent:

ans

-1

I don't understand difference... YES -- I HAVE CLARIFYED solve() uses directly noted variable or create it on flying, and assigning x=.. gives us new var. at same name

Q4: The conclusion become obvious. But no good construction. In general:

Let's x,y real anyway created, needed (x-y) as symbolic ratio. I wish be guaranteed:

sym(0.5-0.8) --> -3/10 %normal

sym(0.6915 - 0.69) --> 211106232533/140737488355328 %wrong

sym(rats(0.5)-rats(0.8)) --> [ 0, 0, 0, 0, 0, 0, -3, 0, -3, 0, 0, 0, 0, 0] %what is it?

sym(0.69315)-sym(0.69) --> 63/20000 % best way

>>a=log(2);a=sym(vpa(a,5));a-sym(0.69)

0.0031471805598357605049386620521545 % again wrong