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If S is a finite series, then the Degree(S, x) calling sequence returns the degree of S with respect to the variable x. If S is an infinite series, then the result is infinity.

The Degree(S, [x1,.., xn]) calling sequence returns [Degree(S, x1),..., Degree(S, xn)].

The Degree(S) calling sequence returns the maximum degree of S with respect to its variables. This allows the user to test whether a series is finite.

$\mathrm{with}\left(\mathrm{OrthogonalSeries}\right)\:$

$S≔\mathrm{Create}\left(\left[\left(0\,0\right)=3\,\left(1\,2\right)=-1\,\left(3\,2\right)=\mathrm{\alpha }\right]\,\mathrm{GegenbauerC}\left(n\,1\,x\right)\,\mathrm{LaguerreL}\left(m\,1\,y\right)\right)$

$S≔3\mathrm{GegenbauerC}\left(0\,1\,x\right)\mathrm{LaguerreL}\left(0\,1\,y\right)-\mathrm{GegenbauerC}\left(1\,1\,x\right)\mathrm{LaguerreL}\left(2\,1\,y\right)+\mathrm{\alpha }\mathrm{GegenbauerC}\left(3\,1\,x\right)\mathrm{LaguerreL}\left(2\,1\,y\right)$

$\mathrm{Degree}\left(S\,x\right)\;$$\mathrm{Degree}\left(S\,y\right)\;$$\mathrm{Degree}\left(S\,\left[x\,y\right]\right)$

$3$

$2$

$\left[3\,2\right]$

$\mathrm{Degree}\left(S\right)$

$3$

$\mathrm{S1}≔\mathrm{Create}\left(\left\{\frac{1}{n^2}\,n=1..\mathrm{\infty }\right\}\,\mathrm{ChebyshevT}\left(n\,x\right)\right)$

$\mathrm{S1}≔\sum _{n=1}^{\mathrm{\infty }}\frac{\mathrm{ChebyshevT}\left(n\,x\right)}{n^2}$

$\mathrm{Degree}\left(\mathrm{S1}\,x\right)\;$$\mathrm{Degree}\left(\mathrm{S1}\,y\right)\;$$\mathrm{Degree}\left(\mathrm{S1}\right)$

$\mathrm{\infty }$

$0$

$\mathrm{\infty }$

$\mathrm{S2}≔\mathrm{Create}\left(\left\{\frac{1}{n^2}\,n=3..8\,\left[0=1\,N=2\right]\right\}\,\mathrm{ChebyshevT}\left(n\,x\right)\right)$

$\mathrm{S2}≔\mathrm{ChebyshevT}\left(0\,x\right)+2\mathrm{ChebyshevT}\left(N\,x\right)+\left(\sum _{n=3}^8\frac{\mathrm{ChebyshevT}\left(n\,x\right)}{n^2}\right)$

$\mathrm{Degree}\left(\mathrm{S2}\right)$

$\max \left(8\,N\right)$