# Set global precision for reals?

Hello,

If this makes any difference, I am using the Sage Notebook.

I want to reuse a large piece of code. However, when I wrote it, the default precision seemed sufficient to me, and now I am encountering truncation errors. Can I specify a global precision at the beginning of the worksheet? My variable declarations are all like a,b=var('a,b').

Thanks!

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If the above is not possible, is it possible to change the default precision for hard-coded constants? For example, I want 12.34.precision() to return some value of my choice. Also, is it possible the result of an operation involving numbers of different precisions to automatically return a number of the higher precision?

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As far as I know there's no way to globally change the precision of computations over the real numbers. However, using RealField you can define variables (real numbers) that will only compute up to a desired precision. First note that Sage's "default" RealField, called RR, has 54 bits of precision:

sage: RR
Real Field with 53 bits of precision
sage: a = RR(1); b = RR(2)
sage: c = a+b
sage: c
3.00000000000000
sage: parent(c)
Real Field with 53 bits of precision


That last line shows that if you add two elements of RR you indeed get an element of RR in return. However, I can define lower precision real numbers like so:

sage: RF = RealField(10); RF
Real Field with 10 bits of precision
sage: a = RF(1); b = RF(2)
sage: c = a+b; c
3.0
sage: parent(c)
Real Field with 10 bits of precision


So the bottom line is that if you make sure that call of your calculations are in the field RealField(prec) then they will be with prec precision. Note that you can define matrices, vectors, polynomial rings, and what have you over RealField(prec) as well:

sage: RF = RealField(10)
sage: M = matrix(RF,[[1,0],[0,1]]); M
[ 1.0 0.00]
[0.00  1.0]
sage: parent(M)
Full MatrixSpace of 2 by 2 dense matrices over Real Field with 10 bits of precision


Finally, the constructor ComplexField is the complex analogue of RealField.

more If you want to see what Sage does when you type in 12.34 into the command line, you can do

sage: preparse('12.34')
"RealNumber('12.34')"


You can see that it's just passing a string version of what you type in to the global function RealNumber. Currently, that just returns a RealNumber object with 53 bits of precision. You can replace that with whatever you want. For example,

sage: R = RealField(100); R
Real Field with 100 bits of precision
sage: RealNumber = R
sage: 12.34
12.340000000000000000000000000
sage: (12.34).parent()
Real Field with 100 bits of precision

more

I was searching anything like this for a long time!! Thanks a lot :) PS: Sorry for my english, that is not my mother tongue.