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

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Howard Padmore
Howard Padmore 2023-6-13
评论： Dyuman Joshi 2023-6-16
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)
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Dyuman Joshi
Dyuman Joshi 2023-6-14
编辑：Dyuman Joshi 2023-6-14
Ran in:
"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 = 

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