Symbolic expressions with pi are displaying as decimals

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Nathaniel H Werner 2024-2-10

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https://ww2.mathworks.cn/matlabcentral/answers/2080576-symbolic-expressions-with-pi-are-displaying-as-decimals

编辑： Paul 2024-2-11

采纳的回答： Walter Roberson

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I am trying to write a livescript that has pi show up a lot in the expressions.

Here is a sample of my script.

clc, clear, close all

syms n x L

S = 3;

R = 0.6;

f1 = S*x; % x < R

f2 = S*R; % R < x < L

fplot(f1,[0 R],'b'), hold on

fplot(f2,[R 1],'b'), xline(R,'--')

ylim([0 ceil(S*R)]), grid on

lambda = (((2*n+1)*pi)/(2*L))^2

lambda =

A_n = 2/L*(int(f1,x,0,R*L)+int(f2,x,R*L,L))

A_n =

You can see the outputs above, but in my script where lamba is output this is the result.

I must have changed the settings at some point, how do I make pi show up as a symbol? If possible rational numbers like the 27/50 should be decimals, but if it's not possible to have both that's fine. My release is 2021b.

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采纳的回答

Walter Roberson 2024-2-10

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sympref('FloatingPointOutput', 0)

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Paul 2024-2-10

编辑：Paul 2024-2-11

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I suspect that preference is, in fact, the issue for the particular problem by the OP, and I always forget about this preference.

But, if I'm not mistaken, this preference only controls the display of expressions but not their internal representation. If correct, this preference is a neccesary condition to have the constant pi in symbolic expressions be displayed as pi, but not sufficient.

sympref('default');
sympref('FloatingPointOutput')
ans = logical
   0

With the default value of false, pi can still be absorbed

f = sym(pi^2/4)

f =

So sym(pi) is still needed

f = sym(pi)^2/4

f =

If the preference is set to true, it does change the display

sympref('FloatingPointOutput',1);
f
f = 2.4674

But not the internal representation

sympref('FloatingPointOutput',0);

f =

TLDR: IMO, use sym(pi) in all symbolic expressions, either explicitly, or defining Pi = sym(pi) at the top of the code and use that, or define a function that returns sym(pi) and use that. Use FloatingPointOutput to control display of symbolic numbers.

Nathaniel H Werner 2024-2-11

Interesting, my run was able to recognize it.

Walter Roberson 2024-2-11

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lambda = (((2*n+1)*pi)/(2*L))^2

n is symbolic, so 2*n+1 is symbolic. symbolic times numeric pi results in numeric pi being converted to symbolic, which converts to symbolic π because there is an exact match to the value it knows as numeric pi. So (2*n+1)*pi converts to

2*L is numeric 2 times symbolic L, which triggers converting numeric 2 to symbolic 2, giving

You now have

which then gets squared.

By way of contrast,

sym(pi^2/4)

evaluates pi^2 numerically and divides by 4 numerically . Then it attempts to convert to symbolic. However, the numeric pattern matching is not able to recognize the result and so converts the result to a symbolic rational number.

Roughly speaking, the symbolic toolbox is able to recognize a/b*pi where a and b are in the range 0 to 999 . It might recognize some other patterns as well.

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Paul 2024-2-10

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Hi Nathaniel.

Option 1: Always use

sym(pi);

in symbolic expressions. For example

5.13445677*sym(pi)

ans =

If you use the numeric pi in an expression and then convert to sym, sometimes the Symbolic Math Toolbox can figure it out, like this

sym(2.5*pi)

ans =

But sometimes it can't

sym(5.13445677*pi)

ans =

So use sym(pi) to be safe.

Option 2: Define a variable that's sym(pi) and just use it everywhere in symbolic expressions

Pi = sym(pi);

5.13445677*Pi

ans =

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DGM 2024-2-11

From @Nathaniel H Werner's comment-as-flag:

"This comment is opinion, and not objectively based. Comments and answers should attempt to give objective answers to the questions not the opinion of the commenter."

There's plenty of room for opinion, but best practices or canonical code patterns aren't really all that subjective. Either way, you're going to have a hard time finding anyone with editor status who would disagree so severely with James on the matter, so flagging his comment isn't going to get any of us to delete it. Besides, it would break the continuity of the thread. If you don't need the attention of an editor or staff, please use a comment instead of a flag.