MATLAB: How to simplify a complex matrix

MATLAB

I am having a polynomial matrix as an e.g.,

A= [1, 0; 0, ((2098771722748011756657413967615*z^2)/2535301200456458802993406410752 - (7700501052346207801164205137339*z)/5070602400912917605986812821504 - 10387006882955487611545293966533/20282409603651670423947251286016]

Best Answer

When you enter numbers like that, they will be converted to double precision, which does not have enough precision for you. You need to change the numbers to symbolic.

syms z
A = [1, 0; 0, ((sym('2098771722748011756657413967615')*z^2) / sym('2535301200456458802993406410752') - (sym('7700501052346207801164205137339')*z) / sym('5070602400912917605986812821504') - sym('10387006882955487611545293966533/20282409603651670423947251286016')]

Related Solutions

MATLAB: MuPad reduce roots

MuPad and Maple don't simplify it like you expect unless you do this:

%matlab syntax
z=sym('z','positive')
simplify((z^3)^(1/3))

ans=

In MuPad use this syntax

assume(z, Type::Positive)
simplify((z^3)^(1/3))

In Maple use this syntax

assume(0 < z)
simplify((z^3)^(1/3))

The reason can be found by testing:

z=-1
(-1^3)^(1/3)
ans =
  0.500000000000000 + 0.866025403784439i
z=1
(1^3)^(1/3)
ans =
     1

Roots of negative values give results with imaginary parts while roots of positive values always return real numbers, in the case provided for all z>0 (and z=0) the simplified expression is z and for all z<0 the simplified expression remains (z^3)^(1/3)

The symbolic engine by default doesn't limit the symbolic variables (type, range of values, etc) so if it simplified the expression to just z that would be incorrect!

MATLAB: How to simplify polynomial expansion

Maple pretty quickly calculates it as the ratio of a cubic divided by a quartic. The coefficients involved are quite large.

You can get very long coefficients such as that if you input floating point numbers, as by default MuPad converts floating point numbers in to rational values. For example, in a problem earlier today someone wanted to use 0.707 which would have led to a _much _messier answer than what the probable value was, 1/sqrt(2)

I have confirmed that the numerator and denominator of the ratio do not have any roots in common (not even close), so it is not possible to reduce the expression to a polynomial instead of a ratio of polynomials.

Best Answer

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MATLAB: MuPad reduce roots

MATLAB: How to simplify polynomial expansion

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