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powseries

 subtract
 subtraction of two formal power series

 Calling Sequence subtract(a, b)

Parameters

 a, b - formal power series

Description

 • The function subtract(a, b) returns the formal power series in which each coefficient is the corresponding coefficient of a minus the corresponding coefficient of b.
 • This function yields the same result as powadd(a, negative(b)), but is faster.
 • The command with(powseries,subtract) allows the use of the abbreviated form of this command.

Examples

 > $\mathrm{with}\left(\mathrm{powseries}\right):$
 > $\mathrm{powcreate}\left(t\left(n\right)=\frac{t\left(n-1\right)}{n},t\left(0\right)=1\right):$
 > $\mathrm{powcreate}\left(v\left(n\right)=\frac{v\left(n-1\right)}{2},v\left(0\right)=1\right):$
 > $s≔\mathrm{subtract}\left(v,t\right):$
 > $\mathrm{tpsform}\left(s,x,6\right)$
 ${-}\frac{{1}}{{2}}{}{x}{-}\frac{{1}}{{4}}{}{{x}}^{{2}}{-}\frac{{1}}{{24}}{}{{x}}^{{3}}{+}\frac{{1}}{{48}}{}{{x}}^{{4}}{+}\frac{{11}}{{480}}{}{{x}}^{{5}}{+}{\mathrm{O}}\left({{x}}^{{6}}\right)$ (1)