MaplePortal/SymbolicMath - Help

 Symbolic Math

Maple lets you manipulate formulas symbolically. For example, here we rearrange the Van der Waals formula

 >
 > $\mathrm{solve}\left(\mathrm{vdw},P\right)$
 $\frac{{n}{}\left({R}{}{T}{}{{V}}^{{2}}{+}{a}{}{b}{}{{n}}^{{2}}{-}{V}{}{a}{}{n}\right)}{{{V}}^{{2}}{}\left({-}{b}{}{n}{+}{V}\right)}$ (1)

Maple contains much more symbolic math functionality. Explore a few more examples below by selecting an item from the list below

 Factor a Polynomial

 > $\mathrm{factor}\left(6{x}^{2}+18x-24\right)$
 ${6}{}\left({x}{+}{4}\right){}\left({x}{-}{1}\right)$ (2)

 Expand Functions and Distribute Products Over Sums

 > $\mathrm{expand}\left(\left(x+1\right)\left(x+2\right)\right)$
 ${{x}}^{{2}}{+}{3}{}{x}{+}{2}$ (3)

 Sort the elements of a list, Vector, or one-dimensional Array

 > $\mathrm{sort}\left(\left[2,1,3\right]\right)$
 $\left[{1}{,}{2}{,}{3}\right]$ (4)
 > $\mathrm{sort}\left(\left[a,\mathrm{ba},\mathrm{aaa},\mathrm{aa}\right],\mathrm{length}\right)$
 $\left[{a}{,}{\mathrm{ba}}{,}{\mathrm{aa}}{,}{\mathrm{aaa}}\right]$ (5)

 Collect coefficients of like powers

 > $g:={x}^{2}{ⅇ}^{x}-2x{ⅇ}^{x}+2{ⅇ}^{x}-\frac{{x}^{2}}{{ⅇ}^{x}}-\frac{2x}{{ⅇ}^{x}}-\frac{2}{{ⅇ}^{x}}:$
 > $\mathrm{collect}\left(g,{ⅇ}^{x}\right)$
 $\left({{x}}^{{2}}{-}{2}{}{x}{+}{2}\right){}{{ⅇ}}^{{x}}{+}\frac{{-}{{x}}^{{2}}{-}{2}{}{x}{-}{2}}{{{ⅇ}}^{{x}}}$ (6)

 Numerator or denominator of an expression

 > $g≔\frac{1+x}{{x}^{\frac{1}{2}}y}:$
 > $\mathrm{numer}\left(g\right)$
 ${x}{+}{1}$ (7)
 > $\mathrm{denom}\left(g\right)$
 $\sqrt{{x}}{}{y}$ (8)

 Series expansion

 > $\mathrm{series}\left(\mathrm{sin}\left(x\right),x=4,5\right)$
 ${\mathrm{sin}}\left({4}\right){+}{\mathrm{cos}}\left({4}\right){}\left({x}{-}{4}\right){-}\frac{{1}}{{2}}{}{\mathrm{sin}}\left({4}\right){}{\left({x}{-}{4}\right)}^{{2}}{-}\frac{{1}}{{6}}{}{\mathrm{cos}}\left({4}\right){}{\left({x}{-}{4}\right)}^{{3}}{+}\frac{{1}}{{24}}{}{\mathrm{sin}}\left({4}\right){}{\left({x}{-}{4}\right)}^{{4}}{+}{\mathrm{O}}\left({\left({x}{-}{4}\right)}^{{5}}\right)$ (9)

 Convert an expression to a different form

 >
 ${\mathrm{polar}}\left(\sqrt{{5}}{,}{\mathrm{arctan}}\left({2}\right)\right)$ (10)
 > $g:=\mathrm{sinh}\left(x\right)+\mathrm{sin}\left(x\right)$
 ${g}{≔}{\mathrm{sinh}}\left({x}\right){+}{\mathrm{sin}}\left({x}\right)$ (11)
 > $\mathrm{convert}\left(g,\mathrm{exp}\right)$
 $\frac{{1}}{{2}}{}{{ⅇ}}^{{x}}{-}\frac{{1}}{{2}}{}{{ⅇ}}^{{-}{x}}{-}\frac{{1}}{{2}}{}{I}{}\left({{ⅇ}}^{{I}{}{x}}{-}{{ⅇ}}^{{-}{I}{}{x}}\right)$ (12)

 Find indeterminates of an expression

 > $\mathrm{indets}\left(xy+\frac{z}{x}\right)$
 $\left\{{x}{,}{y}{,}{z}\right\}$ (13)
 >
 $\left\{{x}{,}{y}{,}{\mathrm{sin}}\left({x}\right)\right\}$ (14)
 > $\mathrm{indets}\left(\mathrm{sin}\left(x\right)\cdot y,\mathrm{name}\right)$
 $\left\{{x}{,}{y}\right\}$ (15)

 Create a sequence of values or expressions

 > $\mathrm{seq}\left({i}^{2},i=1..10\right)$
 ${1}{,}{4}{,}{9}{,}{16}{,}{25}{,}{36}{,}{49}{,}{64}{,}{81}{,}{100}$ (16)
 >
 ${1}{,}{8}{,}{27}{,}{64}{,}{216}{,}{343}$ (17)
 >
 ${"black"}{,}{"mauve"}{,}{"purple"}{,}{"red"}$ (18)

 Solve a differential equation symbolically

 > $\mathrm{eq}≔\left\{\frac{ⅆ}{ⅆt}y\left(t\right)+{\mathrm{sin}}^{2}\left(t\right)=0,y\left(0\right)=0\right\}:$
 > $\mathrm{dsolve}\left(\mathrm{eq}\right)$
 ${y}\left({t}\right){=}\frac{{1}}{{4}}{}{\mathrm{sin}}\left({2}{}{t}\right){-}\frac{{1}}{{2}}{}{t}$ (19)

 Substitute an expression for another expression

 > $\mathrm{subs}\left(a=x+1,\mathrm{foo}=\frac{a+\mathrm{sin}\left(x\right)}{{a}^{2}}\right)$
 ${\mathrm{foo}}{=}\frac{{x}{+}{1}{+}{\mathrm{sin}}\left({x}\right)}{{\left({x}{+}{1}\right)}^{{2}}}$ (20)

 Differentiate or integrate an expression

Differentiate or integrate an expression

 > $\mathrm{diff}\left({x}^{2},x\right)$
 ${2}{}{x}$ (21)
 >
 ${{x}}^{{2}}$ (22)

Details: diff, int

 Limit of an expression

This the the gain of an op amp

 > $\mathrm{gain}:=-\frac{A\left(\mathrm{C1}\mathrm{R2}s+1\right)}{A\mathrm{C1}\mathrm{C2}\mathrm{R1}\mathrm{R2}{s}^{2}+\mathrm{C1}\mathrm{C2}\mathrm{R1}\mathrm{R2}{s}^{2}+A\mathrm{C1}\mathrm{R1}s+A\mathrm{C2}\mathrm{R1}s+\mathrm{C1}\mathrm{R1}s+\mathrm{C1}\mathrm{R2}s+\mathrm{C2}\mathrm{R1}s+1}:$

Compute the limit as $A$ goes to infinity.

 > $\mathrm{limit}\left(\mathrm{gain},A=\mathrm{infinity}\right)$
 ${-}\frac{{\mathrm{C1}}{}{\mathrm{R2}}{}{s}{+}{1}}{{\mathrm{R1}}{}{s}{}\left({\mathrm{C1}}{}{\mathrm{C2}}{}{\mathrm{R2}}{}{s}{+}{\mathrm{C1}}{+}{\mathrm{C2}}\right)}$ (23)