formula.repository

This library defines basic operation on polynomials, and contains also 3 different roots (zeroes)-fi

\form#0:$P(x)$
\form#1:${a_0}+{a_1}x+{a_2}x^2+{a_3}x^3$
\form#2:$[a_0, a_1, a_2, a_3]$
\form#3:$a_0$
\form#4:$r=p+q$
\form#5:$p\leftarrow p+q$
\form#6:$p+q$
\form#7:$r=p-q$
\form#8:$p-q$
\form#9:$p\leftarrow p-q$
\form#10:\[q=\frac{u}{v}\]
\form#11:\[r=u\%v\]
\form#12:$q=\frac{u}{v}$
\form#13:$r=u\%v$
\form#14:\[u\leftarrow \frac{u}{v}\]
\form#15:$\frac{u}{v}$
\form#16:$r(x)=s.p(x)$
\form#17:$p(x)\leftarrow s.p(x)$
\form#18:$s.p(x)$
\form#19:$r=pq$
\form#20:$y = p(x)$
\form#21:$p(x)$
\form#22:$\frac{p(x)}{(x - a)}$
\form#23:$p(a)$
\form#24:$q(x)=\frac{p(x)-p(a)}{(x - a)}$
\form#25:$p(x)=q(x)(x - a)+p(a)$
\form#26:$a$
\form#27:$p(a)=0$
\form#28:$q(x)$
\form#29:$dy=p'(x)$
\form#30:$p'(x)$
\form#31:$p''(x)$
\form#32:$q(z)=\frac{p(z)}{z-x}$
\form#33:\[p(x)=a_0+a_1{x}+a_2{x^2}+...+a_n{x^n}\]
\form#34:\[q(x)=|a_0|+|a_1|{x}+|a_2|{x^2}+...+|a_n|{x^n}\]
\form#35:$p$
\form#36:$a_1..a_n$
\form#37:$q(x)=x^{n}p(x)$
\form#38:$\frac{p(x)}{x^{-n}}$
\form#39:$x^n$
\form#40:$p\leftarrow pq$
\form#41:$p(x)\leftarrow \frac{p(x)}{s}$
\form#42:$r(x)=\frac{p(x)}{s}$
\form#43:$p(z)$
\form#44:$|p(z)|$
\form#45:$x$
\form#46:\[p(x)=-|a_0|+|a_1|x+|a_2|x^2+...+|a_n|x^n\]
\form#47:$(a_0,a_1,a_2,...,a_n)$
\form#48:$C_u$
\form#49:\[C_u=1+max_n(|a_0|,|a_1|,...,|a_n|)\]
\form#50:$G$
\form#51:\[G_p=\left[\frac{|a_0|}{|a_n|}\right]^{\frac{1}{n}}, p(x)=a_0+a_1{x}+a_2{x^2}+...+a_n{x^n}, a_n\neq 0\]
\form#52:$p(x)=ax+b$
\form#53:$-\frac{b}{a}$
\form#54:$p(x)=ax^2+bx+c$
\form#55:\[S=b+\sqrt{b^2-4ac}\]
\form#56:\[D=b-\sqrt{b^2-4ac}\]
\form#57:\[q=\left\{ \begin{array}{ll} -S & \mbox{if} \left| S\right| >\left| D\right| \\ -D & \mbox{otherwise}\end{array}\right. \]
\form#58:\[z_1=\frac{2c}{q}\]
\form#59:\[z_2=\frac{q}{2a}\]
\form#60:$1+\mbox{ETA}>1$