Howto remove complex expressions in syms

Question

metty 2019-1-2

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/437950-howto-remove-complex-expressions-in-syms

编辑： metty 2019-1-2

I have the following example code:

clear all; clc; close all;
syms q1 q2 q3 q4 q5 q6;
assume(q1,'positive'); assumeAlso(q1,'real');
assume(q2,'positive'); assumeAlso(q2,'real');
assume(q3,'positive'); assumeAlso(q3,'real');
assume(q4,'positive'); assumeAlso(q4,'real');
assume(q5,'positive'); assumeAlso(q5,'real');
assume(q6,'positive'); assumeAlso(q6,'real');
syms l1 l2 l3 l4;
assume(l1,'positive'); assumeAlso(l1,'real');
assume(l2,'positive'); assumeAlso(l2,'real');
assume(l3,'positive'); assumeAlso(l3,'real');
assume(l4,'positive'); assumeAlso(l4,'real');
result = -angle(-(sin(q6) + cos(q6)*1i)*(cos(q2 + q3 + q4)*cos(q1) - cos(q5)*sin(q1)*1i + sin(q2 + q3 + q4)*cos(q1)*sin(q5)*1i)*1i)

How can I change the expression into an algebraic form without complex numbers?

EDIT:

I created a better example to show my problem (thank you for simpler representation, madhan ravi):

clear all; clc; close all;
syms q1 q2 q3 q4 q5 q6 l1 l2 l3 l4 real
assume([q1 q2 q3 q4 q5 q6 l1 l2 l3 l4],'positive')
%No complex numbers:
B1 = -atan2(- cos(q6)*(cos(q5)*sin(q1) - sin(q2 + q3 + q4)*cos(q1)*sin(q5)) - cos(q2 + q3 + q4)*cos(q1)*sin(q6), cos(q2 + q3 + q4)*cos(q1)*cos(q6) - sin(q6)*(cos(q5)*sin(q1) - sin(q2 + q3 + q4)*cos(q1)*sin(q5)))
cos(B1)  %complex numbers suddenly appear here
simplify(B1)   %here also

I suspect that these complex numbers were inserted during simplification steps. Can they be removed again?

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Answer 1

madhan ravi 2019-1-2

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/437950-howto-remove-complex-expressions-in-syms#answer_354683

编辑：madhan ravi 2019-1-2

在 MATLAB Online 中打开

When you substitute a number you would also a get a complex number because you multiply with imaginary number i , how would you mean to eliminate them?

syms q1 q2 q3 q4 q5 q6 l1 l2 l3 l4 real
assume([q1 q2 q3 q4 q5 q6 l1 l2 l3 l4],'positive')
result = -angle(-(sin(q6) + cos(q6)*1i)*(cos(q2 + q3 + q4)*cos(q1) - cos(q5)*sin(q1)*1i + sin(q2 + q3 + q4)*cos(q1)*sin(q5)*1i)*1i)

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metty 2019-1-2

To calculate the expression, you would not need complex numbers. E.g. angle is an atan2-function where the imaginary and the real part uses. I could substitute this function manually. However, Matlab might have a function that forces that an expression can be transformed in a way that no complex numbers occur anymore.

metty 2019-1-2