how do I combine terms with a common power in a polynomial

I am using the symbolic toolbox and am new to it. I have taylor expanded an expression that is a function of x and y. Part of the expansion is

y^2/(2*R) + x^2/(2*R*cos(t)^2) + (A*y^3)/(2*R) + (B*y^4)/(8*R) + (A^2*y^4)/(2*R) + (A^3*y^5)/(2*R)

1st 3 terms in y^2, x^2 and y^3 are fine, but y^4 is split into two terms that should be combined. Anyone know how to do this? Code is

syms z x y t R A B

T=taylor(((x^2*(sec(t))^2+y^2)/((R*((1-A*y)+((1-A*y)^2-B*(x^2*(sec(t))^2+y^2))^0.5)))),[x,y],'Order',6)

T1=collect(T,[x y])

T2=combine(T1,'IgnoreAnalyticConstraints',true)

T3=expand(T2)

[Dyuman Joshi]

They are combined in the output from taylor() (as sigma6)

syms z x y t R A B
T=taylor(((x^2*(sec(t))^2+y^2)/((R*((1-A*y)+((1-A*y)^2-B*(x^2*(sec(t))^2+y^2))^0.5)))),[x,y],'Order',6)

T = 

%T1=collect(T,[x y])
%T2=combine(T1,'IgnoreAnalyticConstraints',true)
%T3=expand(T2)

[Howard Padmore]

Thanks. That is true, but you end up with a bunch of sigmas. Best I have so far is

f=taylor(((x^2*(sec(t))^2+y^2)/((R*((1-A*y)+((1-A*y)^2-B*(x^2*(sec(t))^2+y^2))^0.5)))),[x,y],'Order',7)

f1=collect(f,[x y])

f2=combine(f1,'IgnoreAnalyticConstraints',true)

f3=expand(f2)

f4=collect(f3,[x y])

which gives the formula below. This minimizes sigmas. What I really want is to not have the sigmas at all, ie. just mutiply them out. Is this possible?

f4 =

[Dyuman Joshi]

@Howard Padmore did you check my answer?

[Howard Padmore]

Perfect......many thanks!

[Dyuman Joshi]

Glad to have helped!

Answer 1

[Dyuman Joshi]

"What I really want is to not have the sigmas at all, ie. just mutiply them out. Is this possible?"

It is possible.

From the documentation page Abbreviate Common Terms in Long Expressions - By default, live scripts display symbolic expressions in abbreviated output format.

You can turn off abbreviated output format by setting the 'AbbreviateOutput' preference to false.

syms z x y t R A B

%Change the setting
sympref('AbbreviateOutput',false);

f=taylor(((x^2*(sec(t))^2+y^2)/((R*((1-A*y)+((1-A*y)^2-B*(x^2*(sec(t))^2+y^2))^0.5)))),[x,y],'Order',7);
f1=collect(f,[x y]);
f2=combine(f1,'IgnoreAnalyticConstraints',true);
f3=expand(f2);
f4=collect(f3,[x y])

f4 =