Is this a symbolic math bug?

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

[Andrew Newell]

@Igor - In point 1, do you want to simply display log(2) to 5 digits or set b equal to log(2) rounded to 5 digits?

[Andrew Newell]

I don't understand question 2.

[Doug Hull]

It is a best practice to post ONE question per question. It keeps things orderly.

[James Tursa]

This is the decimal representation of the exact value you are using:

>> num2strexact(0.6915 - 0.69)

ans =

1.50000000000005684341886080801486968994140625e-3

The fact that MATLAB only displays 15 significant decimal digits of this does not mean that the underlying number is exactly the displayed result.

Answer 1

[Igor]

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

[Igor]

Two new questions --

Q5

How to easy convert symbolic d-form into r-form?

Q6: new bug?

>> digits(32)

>> vpa(pi,100)

ans =

3.141592653589793115997963468544185161590576171875

>> vpa pi 100

ans =

3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117068

[Andrew Newell]

Igor, can you please make a new question for each of these issues? This sprawling post is hard to deal with.

[James Tursa]

In the case of (0.5-0.8) the sym function is trying to "guess" what you meant by the input. Again, the input is not exactly 0.3, it is:

>> num2strexact(0.5-0.8)

ans =

-0.3000000000000000444089209850062616169452667236328125

So in this case it guessed that you really wanted an exact 0.3 result even though the input was *not* exactly 0.3. But in the other case:

>> num2strexact(0.6915 - 0.69)

ans =

1.50000000000005684341886080801486968994140625e-3

the sym function just wasn't clairvoyant enough to guess what you wanted for a result. Don't blame syms for being "wrong" just because it didn't guess what you wanted as well as you had hoped. Reformulate your code properly instead.

Answer 2

[Andrew Newell]

I think what you want in question 1 is

b = vpa(log(sym('2')),5);

For question 3, x should be the variable in SOLVE:

syms x positive
x = solve('x=-1',x)

For question 4, try

vpa(sym('0.6915')-sym('0.69'),5)

ans =

0.0015

To get the right answer for the fraction, use:

vpa(sym('211106232533/140737488355328'))

You were calculating it in double precision, which isn't accurate enough.

EDIT: I have incorporated a couple of suggestions from @Walter and another from @James.

[Walter Roberson]

Andrew, you are letting things be evaluated by Matlab in double precision before having them pass in to the symbolic engine.

b = vpa(log(sym('2')),5);

vpa(sym('211106232533/140737488355328'))

[Andrew Newell]

Good point, @Walter. I prefer doing my symbolic calculations directly in Maple - fewer pitfalls.