How to stop result being rounded - Symbolic mathematics

Thank you so much for any assistance you can provide.

I am trying to find the time (t > 0) where a function is a maximum, and the integral of the function (0 < t < inf) using symbolic mathematics. Doing this same problem by hand, or using Wolfram-Alpha or using Maple, I get a solution of t = -0.000903 (which we disregard) and t = 0.00168. The value of the integral is 0.00297. With MATLAB, I get a solution of t = -9.3e-04 (which we disregard) and t = 0.00170. The value of the integral is 0.0030. I understand that the MATLAB solutions are merely a rounded version of the other answers, but I cannot seem to change the way the results are displayed to the command window to obtain the final solutions I expect of t = 0.00168 and the integral of 0.00297.

After reading through other forums, I have tried to use the vpa command (see below) and I have tried to alter the way the result is displayed on the command windown using fprintf.

syms t
%Describe the voltage and current functions
v=(10000*t+5)*exp(-400*t);
i=(40*t+0.05)*exp(-400*t);
%Obtain power
p=i*v;
%Obtain the derivative of the power and the time(s) when the derivative is zero
deriv_p=diff(p);
t_when_deriv_p_is_zero=solve(deriv_p == 0, t)
%Attempt to increase the number of digits displayed using vpa
t_when_deriv_p_is_zero=vpa(solve(deriv_p==0),6)
%Obtain only values of time when t>0 
%Attempt to increase the number of digits displayed using vpa
t_of_max_p_1=vpa(t_when_deriv_p_is_zero(t_when_deriv_p_is_zero>0),6)
t_of_max_p=t_when_deriv_p_is_zero(t_when_deriv_p_is_zero>0)
%Attempt to increase the number of digits displayed using fprintf
fprintf('%1.5f\n', t_of_max_p_1)
fprintf('%1.5f\n', t_of_max_p)
%Obtain the total energy through integration of the power
%Attempt to increase the number of digits using vpa and fprintf
w_total=vpa(int(p,t,0,inf),6)
w_total=int(p,t,0,inf)
fprintf('%1.5f', w_total)

Thank you for helping me understand MATLAB a little better!!

[Torsten]

You mean something like

fprintf('%1.10f\n', double(t_of_max_p_1))

?

Answer 1

[Walter Roberson]

No problems here.

syms t positive
%Describe the voltage and current functions
v=(10000*t+5)*exp(-400*t);
i=(40*t+0.05)*exp(-400*t);
%Obtain power
p=i*v;
%Obtain the derivative of the power and the time(s) when the derivative is zero
deriv_p=diff(p);
t_when_deriv_p_is_zero=solve(deriv_p == 0, t)

t_when_deriv_p_is_zero = 

%Attempt to increase the number of digits displayed using vpa
t_when_deriv_p_is_zero=vpa(solve(deriv_p==0),6)

t_when_deriv_p_is_zero = 

0.00168004

%Obtain only values of time when t>0 
%Attempt to increase the number of digits displayed using vpa
t_of_max_p_1=vpa(t_when_deriv_p_is_zero(t_when_deriv_p_is_zero>0),6)

t_of_max_p_1 = 

0.00168004

t_of_max_p=t_when_deriv_p_is_zero(t_when_deriv_p_is_zero>0)

t_of_max_p = 

0.001680038313613796407963718593237

%Attempt to increase the number of digits displayed using fprintf
fprintf('%1.5f\n', t_of_max_p_1)

0.00168

fprintf('%1.5f\n', t_of_max_p)

0.00168

%Obtain the total energy through integration of the power
%Attempt to increase the number of digits using vpa and fprintf
w_total=vpa(int(p,t,0,inf),6)

w_total = 

0.00296875

w_total=int(p,t,0,inf)

w_total = 

fprintf('%1.5f', w_total)

0.00297

[Christine Zakzewski]

Thank you so much for reviewing my code. I ran your modifed code (with the "syms positive" added. I am, unfortunately, still getting the same rounded results,.

t_when_deriv_p_is_zero =

0.0017

w_total =

0.0030

So it is not the code. I have also tried to change the numeric format through the Preferences>Command Window and that did not help. Could it be my settings? (For example, I never see a result with a square root like you show above)

[Walter Roberson]

You would see the fancy output if you ran the code in Live Script.

When I run in R2021a (your version) on my Mac, and not in Live Script, I get

t_when_deriv_p_is_zero =

109^(1/2)/8000 + 3/8000

t_when_deriv_p_is_zero =

0.00168004

t_of_max_p_1 =

0.00168004

t_of_max_p =

0.001680038313613796407963718593237

0.00168

0.00168

w_total =

0.00296875

w_total =

19/6400

0.00297

[Christine Zakzewski]

I ran the code in LiveScript and got the same rounded results. Ugh. Its obviously not the code, so its something on my end - some setting/preference is not right.

[Christine Zakzewski]

And, also, Walter Robinson, I wanted to tell you that I have learned so much from you over the past few years of being a part-time dabbler in MATLAB. I am so greatful to you for sharing your time and expertise.

[Christine Zakzewski]

Sorry I mistyped your last name - excuse me - Walter Roberson !

[Steven Lord]

Can you show us the output of the sympref function?

[Christine Zakzewski]

>> sympref

ans =

struct with fields:

FourierParameters: [1×2 sym]

HeavisideAtOrigin: [1×1 sym]

AbbreviateOutput: 1

TypesetOutput: 1

FloatingPointOutput: 1

PolynomialDisplayStyle: 'default'

MatrixWithSquareBrackets: 0

[Christine Zakzewski]

Here are some things I experimented with

>> t_when_deriv_p_is_zero(2)

ans =

0.0017

>> t_when_deriv_p_is_zero(2)*10000

ans =

16.8004

>> vpa(t_when_deriv_p_is_zero(2),10)

ans =

0.0017

>> vpa(t_when_deriv_p_is_zero(2)*100000,10)

ans =

168.0038

>> double(t_when_deriv_p_is_zero(2)

ans =

0.0017

>> double(t_when_deriv_p_is_zero(2)*1000)

ans =

1.6800

[Steven Lord]

Try changing the values of the 'AbbreviateOutput' or 'FloatingPointOutput' preferences and check if the behavior changes.

sympref('default');
P = sympref % Default values

P = struct with fields:
           FourierParameters: [1    -1]
           HeavisideAtOrigin: 1/2
            AbbreviateOutput: 1
               TypesetOutput: 1
         FloatingPointOutput: 0
      PolynomialDisplayStyle: 'default'
    MatrixWithSquareBrackets: 0

sympref('AbbreviateOutput', false);
P2 = sympref

P2 = struct with fields:
           FourierParameters: [1    -1]
           HeavisideAtOrigin: 1/2
            AbbreviateOutput: 0
               TypesetOutput: 1
         FloatingPointOutput: 0
      PolynomialDisplayStyle: 'default'
    MatrixWithSquareBrackets: 0

[Christine Zakzewski]

Hallelujah! That works now!

Thank you for your help!

[Christine Zakzewski]

I ended up deleting all the files from the preferences folder (except the history files), and that solved the issue as well. After deleting the preferences folder, I changed the sympref file back to default and now the program is working as expected, and the results are exact solutions. I assume this means there was something changed in the preferences folders (although I do not use MATLAB enough to go around messing with preferences intentionally!).