please let me have a help with the 'solve' command

in the following is:

i = sqrt(-1)
pi= 3.1416
syms m fi real
assumeAlso( fi>=0 )
assumeAlso( fi<2*pi )

31-december-2016

Dear Sir

please let me have a help with the 'solve' command.

I have two running installation, one is matlab R2009a and the other is matlab R2016a.

So , i noted a different behavior of the command 'solve' between the two version of matlab when i attempt to solve this little equation:

m*exp(i*fi) = -2

with the constraint that both m and fi must be real.

This equation has only 2 sets of real solutions:

1st set : {m=-2 fi=0}

2nd set : {m=2 fi=pi}

now , the R2009a find exactly this sets of solutions, instead the R2016a not.

I tried including some parameter in the command string , such as 'IgnoreAnalyticCostraints' or 'MaxDegree', but i was not able to force R20016a to obtain these complete solutions.

Please take a look at the image screenshot here enclosed where show both Matlab versions at work , with the different solutions obtained, note R2061a obtain only the 1st set : {m=-2 fi=0}

please let me know the right steps for obtain the solution {m=2 fi=pi} also in the R2016a

Thank you

Kind Regards

[e-mail]

Answer 1

[Walter Roberson]

"This equation has only 2 sets of real solutions:"

That turns out not to be correct.

[FI, M, P, C] = solve(m*exp(i*fi)==-2, 'ReturnConditions', true)
FI =
 pi + 2*pi*k
      2*pi*k
M =
  2
 -2
P =
k
C =
 in(k, 'integer')
 in(k, 'integer')

so there are real solutions for every odd multiple of pi with M = 2, and there are real solutions for every even multiple of pi with M = -2

The fact that solve() could not return those in the forms of command you used is a bug, which I have just reported with a number of test cases showing various weaknesses.

The best approach so far is to use the multiple output form, allowing one output for each variable, plus one output for parameters, plus one output for conditions, and in solve() to list all of the variables in the order you want them output, and use ReturnConditions true

[M A]

In my original submission i forgot to include in the heading these two statements

>> assumeAlso( fi>=0 )

>> assumeAlso( fi<2*pi )

moreover using for the 'solve' command the forms as You suggested, now the code run fine, here is one example

>> syms m fi real

>> assumeAlso( fi>=0 )

>> assumeAlso( fi<2*pi )

>> [FI, M, P, C] = solve(m*exp(i*fi)==-2, 'ReturnConditions', true)

FI =

0
pi

M =

 -2
  2

P =

Empty sym: 1-by-0

C =

 TRUE
 TRUE

>>

thankyou very much mr Roberson

thankyou very much mr Strider

Answer 2

[Star Strider]

There have probably been some version changes in the solve function in the last 7 years.

This works (in R2016b):

syms m fi real
Eqn = m*exp(i*fi) == -2;
[m,fi] = solve(Eqn)

m =
 pi
  0

fi =
  2
 -2